Was it possible for a message from Paris to reach London within 48 hours in 1782?

Pigeons are way faster:

Their average flying speed over moderate 965 km (600 miles) distances is around 97 km/h (60 miles per hour) and speeds of up to 160 km/h (100 miles per hour) have been observed in top racers for short distances.

Where the direct distance from Paris to London is 344 kilometers (214 miles).

Therefore: 344km / 97km/h = 3.546391753h, which is roughly 4 hours.

One has to consider the weather and that they also make breaks.

The mere limitation is that a pigeon can only carry up to 75 g (2.5 oz).

Also birds of prey might occasionally cancel the delivery.

And I've dug up this article, concerning France & England (about 100 years later):

It is save to assume that this service existed long before it had been commercialized and was made available to the general public. Who had access to the service in 1782 wasn't part of the question.

Paul Reuter would be another example for using the same route, but a little earlier.

No idea if the story occurred exactly as described, but FWIW it is plausible.

Louis XVI sought to flee his plight during the French Revolution a few years later. A number of things went wrong after he left with his family during the night: he opted for a slow, heavy coach instead of the two light ones that had been recommended to him so the family wouldn't be split up; and they had to take care of some repairs along the way. (If memory serves me well they also waited a bit at one of the rendezvous points.)

Anyway, the point is they weren't moving as fast as they could, and when the king was finally unmasked the next day, he and his family were in Varennes, which is to say around 250km away from Paris. Calais is about 300km from Paris. Throw in an extra day to sail to London directly, or to sail to Dover and hurry to London on land, and 48h seems quite plausible.

Post stages existed in France (and elsewhere in Europe) before the Revolution

• where horses would be exchanged along the route

The Wikipedia article Stage station deals more about the 19th century than the 18th century, but otherwise gives a good overview on how the system worked. It also explains the Origin of the name posting:

Medieval couriers were caballari postarus or riders of the posts. The riders mounted fresh horses at each post on their route and then rode on. Post came to be applied to the riders then to the mail they carried and eventually to the whole system. In England regular posts were set up in the 16th century.

The riders of the posts carried the government’s letters. The local postmasters delivered the letters as well as providing horses to the royal couriers. They also provided horses to other travellers.

It was intended not only for carriages, but also for individual travelling and for messengers.

The messenger would start in Paris and regularly change horses on the way to Calais

• the greatest danger was getting a lowsy horse in exchange

So a messenger could, for the time, travel swiftly between

• Paris -> Calais
• Dover -> London

the unknown factor was then only the weather and tide conditions for crossing the Channel using the packet boats or other services that may have been available.

Tour from London to Paris (July 1790) gives the crossing times as

• about 3 hours, with a rough passage (Dover -> Calais)
• 5 hours, 11 PM to 5 AM (Calais -> Dover)
  • plus 2 hours waiting for the tide in Calais
  • due low water in Dover
    • last half mile on an extra boat was needed
  • arrival in Calais at 4 PM
  • left Dover for London 12 noon

From the History of Transport and Travel:

Carriages: 17th century
Coaches gradually become more comfortable. The most common design, developed in Germany in about 1660, is known as the berlin. The compartment for the travellers has the shape of a shallow U, with a protective roof above. There is a door on each side and the coach can seat four people, in pairs facing each other. The coachman, driving the horses, sits above the front wheels.

From 1680 glass windows keep out the weather, where previously there were only blinds. The first simple suspension, protecting the occupants against the bumps of the road, consists of leather straps on which the compartment hangs from the framework. The berlin introduces curved metal springs, which absorb the shocks more effectively.

• Flight to Varennes (1791) of Louis XVI and Marie-Antoinette

Following the aborted trip to Saint Cloud, von Fersen revived these plans with vigor. In June, he acquired a Berline and drove it to a courtyard at Eleanore Sullivan's residence on the Rue de Clichy in Paris. The escape was arranged to take place on 20 June, coinciding with a particular guard change.

Fersen had urged the use of two light carriages that could have made the 200-mile journey to Montmédy relatively quickly. This would have involved the splitting up of the royal family, however, thus Louis and Marie-Antoinette decided on the use of a heavy and conspicuous coach drawn by six horses.

Due to the cumulative effect of slow progression, time miscalculations, lack of secrecy, and the need to repair broken coach traces, the royal family was thwarted in its escape attempt after leaving Paris. Louis himself chatted with peasants while horses were being changed at Fromentieres and Marie Antoinette gave silver dishes to a helpful local official at Chaintrix. At Châlons townspeople reportedly greeted and applauded the royal party. Finally, Jean-Baptiste Drouet, the postmaster of Sainte-Menehould, recognized the king from his portrait printed on an assignat in his possession. Seven detachments of cavalry posted along the intended route had been withdrawn or neutralized by suspicious crowds before the large and slow moving vehicle being used by the royal party had reached them. The king and his family were eventually arrested in the town of Varennes, 50 km (31 miles) from their ultimate destination, the heavily fortified royalist citadel of Montmédy.

Stagecoach and post chaise: 17th - 18th century
Travel between towns by public transport, in the 17th and 18th century, is a slow business. The stagecoach, a heavy and cumbersome carriage often without any form of springs, is introduced in Britain in 1640.

Up to eight of the more prosperous passengers can be packed inside a stagecoach. Second-class seats are available in a large open basket attached to the back. The least privileged travellers sit on the roof with the luggage, relying on a hand rail to prevent themselves slithering off. This immensely unwieldly vehicle, drawn by either four or six horses, lurches along the rutted roads at an average speed of about four miles an hour. Danger from highwaymen is only one of many inconveniences on such a journey.

• The Pickwick Papers has a chapter about how 'fun' this was

Their travels throughout the English countryside by coach provide the chief theme of the novel. A distinctive and valuable feature of the work is the generally accurate description of the old coaching inns of England.

...
The noble and the rich, such as young men on their way through Europe on the Grand Tour, travel in greater comfort - in private, and in well-sprung upholstered carriages. Their favoured vehicle is the post chaise, introduced in France in the early 18th century. Its name accurately suggests a pleasant seat, and an expectation of lively new horses at each post stage during the journey.

From Tour from London to Paris (July 1790)

• Dover -> Calais : about 3 hours, rough passage
  • Chapter 1
• French coinage (conversion rate to Sterling) and measurements
  • Chapter 2
• Calais -> Paris four days and four hours
  • stage coach drawn by 8 horses
  • Chapter 3
• Paris -> London
  • 89 hours, 'which is 19 hours short of time commonly allowed for the performance thereof'
  • Chapter 24

Sources:

• Stage station
• packet boats
• History of Transport and Travel
  • The Pickwick Papers, Charles Dickens, 1836
  • Louis_XVI_of_France
    • Flight to Varennes, 1791
    • Axel von Fersen the Younger
• Dr. Stearns's Tour from London to Paris (1790) - Google Books
  • Samuel Stearns (1741-1810)

The French Postal Service started operation in the fifteenth century and by 1632 - 150 years before your inquiry - there was already a network of over 623 coaching inns operated by it across the length and breadth of France - typically about seven miles apart. These coaching inns provided refreshment, accommodation and fresh teams for all travelers, not just the postal service, who could pay for the service. Anyone with sufficient means and motivation could obtain a fresh horse at each such inn along all major routes - the post roads also first mapped in 1632 - in France.

So in answer to your question - absolutely it was possible to make such a journey in 48 hours. A good riding horse can maintains a working gait (a trot for most breeds) for hours at a time of about 13 to 19 kph (8 - 12 mph). Even at the lower end and allowing time every couple of hours for refreshment and a change of mount, the 300 km from Paris to Calais could be managed in about 25 hours or so (300 km / 12 kph).

A similar calculation for the post road from Dover to London gives a travel time of about 11 hours (132 km / 12 kph) plus the (at most six hours) time to await a sailing tide at Calais still leaves 48 - 21 - 12 - 6 = 9 hours for:

• arranging a ferry; and

• the actual sail from Calais to Dover, a distance of about 50 km or 26 nautical miles which could be traversed easily (provided a fair breeze, preferably a beam reach) at about 4 or 5 knots in 5 to 6 hours.

Note that choosing a trot speed just below the typical range (12 kph instead of 13-19 kph) really slows down the passage - but implies obtaining a dobbin, at a bargain price, rather than the quality steeds available at an extra charge. Those horses could even be ridden at a fast canter (16-27 kph) or even a slow gallop (35-40 kph) and changed at every post-station (15-20 minutes!) or two instead of every three or four hours. If affordable this option would enable taking even 15-20 hours off the time taken.

These coaching inns were not small establishments. Here are 1875 photos of one of the last surviving "galleried" London coaching inns, the Oxford Arms in Warwick Lane near St. Paul's, built in the 1600's and demolished the following year:

Looking across the courtyard:

Looking into Warwick St. from the courtyard: