people had been working on gas turbines for years. See for one example.
There are several paragraphs on gas turbines in the engineering section of "The Naval Annual 1913" edited by Viscount Hythe for example. They knew about the theory and were wondering where it would lead even if it wasn't practical yet.
However there were several problems, one was that industrial or marine turbines were at least an order of magnitude heavier than aircraft engines for the power produced and the 2nd was that the compressors were horribly inefficient. Early experimental engines barely ran, the compressors needing all the power the turbine could generate, leaving little or no power for the output shaft. This did influence later evaluations negatively.
Like I said, the concept was simple. Simply stack axial compressor stages to get the compression ratio you want, stick in a (or more than one) combustion chamber and send the exhaust threw the turbine section to power the compressor, power a shaft and exit the engine producing thrust.
Trouble was that you could not
just stack the compressor sections. Each section needed different pitch blades and stators and often different diameters (volume in the stage) to actually work. At times one (or more stages) actually decreased the compression of the stage/s ahead of it.
Even in the early 1920s there was much discussion on compressors and the US actually built a test flew a plane using a Roots supercharger to compare to centrifugal supercharger. The Roots supercharger was better than no supercharger but that was about it. Most aircraft superchargers of the 1920s and early 30s were not offering even 2 to 1 compression ratios.
So that was step #1. Get a compressor section that will allow the engine to start, run and stay running. You can't even work on the combustion chambers if the compressor won't supply air (well you can using a large industrial compressor but then?). Granted a turbojet doesn't have a turbine sucking power out of the exhaust stream like a turboshaft/turboprop does.
For some reason there were engine designers/companies that tried to build turboprops before they had working turbojets. Yeah, let's design a more complicated turbine section and high power reduction gear before we even get the basic engine to run
Whittle did keep it as simple as possible although the burner/combustion chamber was bit much. But again, you needed a working burner/combustion chamber to study before you could make modifications.
More money could help but more money sometimes isn't going to speed up development of alloys or some other parts much. And even if you can get something to work in a tool room example, can you mass produce it?