Well Airspeed had a licences for the DC-2......
Your problem is all the suggestions so far are...well..shite compared to the DC3.
It needs an earlier realisation that the UK aircraft are far behind the opposition.
Even the Fairey FC1 would be at a disadvantage with 4 engines compared to 2 on the DC-3.
The closest would be the De Havilland Flamingo....but it definately needs a better name.
Fortunately it looks as if Airspeed had licences on the DC-3 too.
According to the Putnams on Airspeed aircraft the firm concluded a licence agreement with Fokker in January 1935. It allowed Airspeed to build Fokker aircraft and sell them in the British Empire and also build and sell the Douglas DC-2 in Britain for which Fokker held a licence for Europe. It then gives a list of the Airspeed designations for the Fokker aircraft as follows:
A.S.16 Fokker F.XXII
A.S.17 Fokker D.XVII
A.S.18 a variant of the A.S.17
A.S.19 Fokker D.XIX
A.S.20 Fokker F.XXXVI
A.S.21 Fokker D.XX
A.S.22 Fokker C.X
A.S.23 Douglas DC-2
However, it also says that a possible contract for 12 Douglas DC-3s for British Continental Airways in late 1936 had to be turned down because the firm was busy with other work. If that is correct the POD could be that Airspeed had a bigger factory or that it wasn't busy with other work.
Late 1936 is also around the time that 80 Bristol Bombays were ordered from Short & Harland. However, the first aircraft didn't fly until March 1939 and ended in June 1940 after only 50 of the 80 aircraft had been built. In addition to buying a handful of D.H.95 Flamingoes for the King's Flight and No. 24 Squadron the RAF also ordered 30 De Havilland D.H.95 Hertfordshires but only one was built and delivered in June 1940.
IMHO there is the opportunity for a swap. That is Airspeed accepts the order for 12 DC-3s from BCAW and the Air Ministry orders 110 Dakotas from Airspeed between 1936 and 1939 instead of the Bombays and Hertfordshires.
The above probably means that Airspeed built fewer Oxford twin-engine trainers. According to Putnams RAF Aircraft Since 1918 a total of 400 were delivered including 75 by De Havilland. A grand total of 8,586 Oxfords were built between November 1937 and July 1945 made up of 4,411 from Airspeed's Portsmouth factory, 550 by Airspeed at Christchurch, 1,515 by De Havilland, 750 by Standard and 1,356 by Percival.
I think the solution is to reduce the Oxford contracts placed with Airspeed and increase the number ordered from De Havilland. Space can be made by not ordering the 250 De Havilland Dons (only 50 build and only 30 of those delivered) and the 30 Hertfordshires. Short & Harland received an order to build Handley Page Herefords (Hampdens fitted with Napier Dagger engines) so the first solution would be to order 80 extra Hampdens in place of the Bombays. However, I think it would be better if Short & Harland had built 75 Sunderlands in place of the 50 Bombays and 100 Herefords that it built IOTL.