Have to admit I have been trying to resolve this one myself, and the issue that keeps coming up to haunt me is the airframe the engines are going to have to be mounted on.
At the beginning of the process, when Whittle had the big idea, the RAF were just phasing out the Bristol Fighter. The main carrier fighter was the Fairey Flycatcher. the standard heavy bomber and Trenchardian hope was the Vickers Virginia.
The idea of any of these, or advanced variants thereof, with jet power would be like trying to fit a CVN's propulsion system to a seventy-four. It just won't go; the aircraft suitable for jet power do not yet exist.
There would probably be a 1900-1910 like explosion of oddities, something very like the pioneer days as everybody tries out what seems to be a good idea to absorb and use the power of even an early jet, in weird and probably not very wonderful configuration.
I suspect the job of being a jet aircraft test pilot in the early thirties would be bloody dangerous- with casualty rates similar to the pioneer aviators more likely than not.
Oh, and on the issue of support for Whittle, the biggest initial problem he had was that the official responsible for evaluating his work was not a dunce or a ministry stooge, but a rival; A A Griffith was a turbine expert himself, and thought Whittle was heading for a blind alley, that axial flow had much greater potential.
Griffith dismissed Whittle's work on those grounds- making a mistake in the calculations didn't help, but ultimately Griffith's case was that Whittle was proposing at best an interim solution, that would ultimately leave Britain at a crippling disadvantage when others developed axial flow and leapt ahead.
The flaw in Griffith's plan turned out to be that centrifugal flow jets proved to be an essential phase in the development of the turbine engine, so much so that it would probably not have been possible to go straight to axials, not if anything like service reliability was to be had.
Unfortunately, it looks to me as if high powered propeller engines were an essential step, too. Without the all metal monoplane generation, without that design and production experience, what is there that can take a jet?
(Edit- bonedome got to that before I did. Damn my slow typing.)