The British were interested in night bombing, an escort fighter was not their game at the time. The jet fighters were pursued as a 'next generation' of fighters, to replace Spitfire and future Typhoon/Tornado, in role of (short range) interceptors.
Start the jet fighter program there after BoB, don't wait another 2 years.
I think you are missing the point (easy to do, I do tend to off on tangents
Gloster
started work on the Meteor in 1940, by early 1941 a contract was placed for 12 prototypes to handle the variety of jet engines under development. DH built the Vampire to specification E.6/41.
How much quicker do you want?
Meteor was a twin engine aircraft because, like the He 280 and the Me 262, no
single engine offered enough thrust
at the time work started to give the desired performance.
Supermarine had given the Air Ministry fits in 1938/39 getting the Spitfire in production and working with the shadow factories. Several other Supermarine project proposals had been turned down because the Air Ministry didn't think Supermarine could deliver on time. Then the British really wind up in a bind. The Hurricane runs into the wall as far as development goes. It
needs the Merlin XX just to get
close to the performance of a Spitfire I or II. The Vulture/Sabre/Centaurus are all running late or coming apart in mid-air (or both) so the BIG Hawker fighter that was
supposed to replace both the Hurricane
and Spitfire is just trickling into service and causing a host of problems. Let's not forget that the TWO most produced Spitfires (the MK V and the MK IX) were BOTH hasty improvisations because Supermarine either hadn't completed work on the more thorough
updates or couldn't convert the production lines in a timely fashion or a bit of both.
As another indication of Supermarine's ability (or lack of) to handle multiple programs lets remember that the
idea of a Griffon powered Spitfire was first brought up in Dec of 1939 in a company Brochure. It took until the end of Nov 1941 to get a flying example and it took another year to start delivering 'production versions' which used MK VC and MK VIII airframes. Building 55 or so MK XII Spitfires with Griffon engines and the same fuel tanks as a MK I Spitfire sure doesn't look like good planning, The last 45 got the wing tanks of the MK VIII.
Having Supermarine trying to design a jet fighter at this time either means a
looong drawn out design development period and/or delays in newer Spitfire models.
Joseph Smith and crew did an amazing job in constantly updating/upgrading the Spitfire beyond what the Air Ministry though possible but they were spread thin as it was.
You had brought up the jet bombers, I was trying to show you that
at the time the power needed for an
allied bomber required more engines than for a German bomber because the allies had to fly further (carry more fuel) than the Arado 234.
An Arado 234B with 2 Jumo engines carried 825 imp gallons of fuel inside and if carrying a 3300lb bomb load it's 'range' was 684 miles. Clean it was 1013 miles.
The larger diameter Allied engine available
during and just after the war are going to hurt performance compared to the narrower German engines. The J-35 Axial engine used in the American bombers was 953mm dia and weighed 1100kg. Off course one engine was offering the thrust of two if the early engines.