score:36
The definitive source you are looking for here would be the Royal Air Force Operations Record Books for the squadrons involved.
There are two parts to RAF Operations Record Books. There is the (usually) monthly 'diary' of the squadron's activities titled ‘detail of work carried out’, recorded on a collection of pre-printed 'Form 541' pages, and a monthly ‘summary of events’ recorded on 'Form 540'. These documents may be completed by hand or typed (or a combination of both).
The UK National Archives have helpfully provided sample pdf files on their website, to give you an idea of what is recorded on each.
I had cause to research this raid some years back. As far as I could find, only 43 bombers, from 6 squadrons, took part in the raid on Berlin on 25-26 August 1940 (although by no means did all aircraft reach their target due to adverse weather conditions!).
The Operations Record Books were originally held in Air Ministry series AIR 27.
Since I did my research on this project, the series has been digitised, and the records are now available to download as pdf files (each file currently costs £3.50 unless you are viewing from a computer at the UK National Archives at Kew. However, there is a preview option that allows you to read some of the details from each file for free).
I have verified the UK National Archives record numbers for each of the files, and included them as links with each squadron below in case you are interested in downloading copies.
From my notes, the squadrons involved were:
51 Squadron
61 Squadron
78 Squadron
99 Squadron
144 Squadron
149 Squadron
The aircraft types involved were (again from my notes):
Armstrong Whitworth Whitley bombers
Handley Page Hampden bombers
Vickers Wellington bombers
(Image sources Wikimedia)
The breakdown by squadron was as follows:
51 Squadron
61 Squadron
78 Squadron
99 Squadron
144 Squadron
149 Squadron
From my notes, it appears that 44 Squadron were involved in attacks on a power station (designated target B57) and an aerodrome (designated target H324) on 25/26 August 1940. 50 Squadron were also involved in the attack on target B57. Most of the aircraft were unable to locate their targets (and many were even unable to locate their secondary targets).
I wasn't able to identify these targets at the time (this was in the early 1990s, long before the operational records were digitised, so we were working with paper files, many of which were either missing or incomplete). It is entirely possible that these targets were located in the vicinity of Berlin. If that is the case, that might explain the figures of 81/95 aircraft that are often quoted online.
It may now be possible to identify these targets using records that have been digitised since I did my research if anyone has the time.
According to this website, 45 Squadron were indeed in North Africa at that time, being based at Helwan in Egypt, with detachments at Erkoweit and Wadi Gazouza in Sudan.
Upvote:2
As an addition to the excellent answer we have, the Bomber Command War Diaries, ed. Martin Middlebrook and Chris Everitt, Midland Publishing, 1996, do have some basic details of the damage done.
Berlin was covered in thick cloud, which prevented accurate bombing, and a strong headwind was encountered on the return journey. The Hampdens were at the limits of their range in these circumstances, and three were lost, three more coming down in the sea due to fuel exhaustion.
The only bombs that fell within the boundaries of Berlin destroyed a wooden summer-house in the suburb of Rosenthal and slightly injured two people. Many bombs fell in the country to the south of Berlin, some on large farms owned by the city. The city residents' joke was that it was an attempt to starve them.
However, the raid had some psychological effect, as described by William Shirer, an American journalist working in Berlin. The population had been assured that Berlin would never be bombed, but aircraft were heard overhead, and the flak fired ineffectively.