I think you have enough time, but there is a not insignificant risk of missing your connection. You are flying with British Airways, who recommend a minimum connection time between the airports of three hours. Since you have 4:25, this is on paper, plenty of time.
Since you’re American, you’ll be able to use the ePassport gates at Heathrow, joining the same queue as UK and EU citizens, which means immigration shouldn’t take too long. It should be no more than half an hour, and probably much quicker.
At that time of day, the coach should take an hour, but if there is bad traffic on the M25, then you could be significantly delayed. In ideal circumstances, I would guess you will get the 7:40 coach, arriving at Gatwick three hours before your next flight. You can be delayed by even 90 minutes by traffic and you will still be OK.
The only issue I can see is that there do not seem to be many flights from London to Dubrovnik. The flights seem to be seasonal, and you haven’t said when you’re flying, but it’s possible that you might need to wait until the flight the next day. In this case, BA ought to pay for your hotel, but it might be advisable to check your travel insurance covers this situation.
If you do miss your connection, you should contact British Airways customer service for rebooking. If you know you are going to be late before you arrive at LGW, I’d recommend phoning BA as soon as possible. And if your flight is delayed at JFK, again, contact airline staff as soon as possible. They may be able to rebook you on a better route from JFK.
It doesn’t leave a massive amount of leeway in case of disruption to the flight into LHR, but it is likely to be enough in practice unless that flight is delayed by more than an hour or so.
The usual rule of thumb I apply when travelling internationally to/from major airports is to arrive at the departure airport 2 hours before take-off, and not to book travel from the arrival airport less than 1 hour after landing. However I would generally allow more time if I knew I had to go through immigration (as a non-citizen of the country/customs area) as queues for this can be long at times.
The ‘2 hours before departure’ rule is probably the one you can push slightly more, especially as you can buy express security if you are running late (but there is usually no way to skip the immigration queue).
If you made a through booking and were not explicitly told that the connections were at your own risk then, in any case, you would be entitled to be booked onto another flight if you miss the connection. Understandably it’s not an ideal situation, but there is backup.
Credit:stackoverflow.com‘