While it might seem simple, creating a grass airfield in Britain was a complicated process to ensure a workable airfield.
Site selection - preferably an area with a convex contour to minimise drainage requirements. Right soil type. Access and amenities also taken into account.
Site clearance - hedge removal, ditch filling, timber removal etc. (agricultural field sizes then were much smaller than today or in the US even then)
Removal of hillocks and depressions with machinery
Consolidation of landing areas with roller
Light ploughing to 6"
Selection of grass mixes to be sown taking account of site, weather conditions and soil conditions.
New grass was then cut at 4"
Field drainage would have to be installed to suit the site and to ensure it could be used all year round.
The test for smoothness of the finished article was a sophisticated comfort test of driving a car across it at 20mph!
Grass fields were fine until aircraft weights began to increase from the late 1930s. Then added to that was the much increased usage of wartime which began to cause problems with surfaces becoming cut up in winter causing undercarriage collapses.
1938 saw the first hard runways installed at Odiham & Gosport which were particularly wet as grass strips. By the end of that year hard runways were seen as essential in light of increasing aircraft weights and work began on 8 fighter airfields in 1939 and then on existing bomber strips by the end of 1940. But it took some time to ensure all existing airfields got them. Training fields came further down the priority list. Often a starting point was a hard perimeter track.
In 1944, in the run up to D-Day a significant number of temporary airfields were required in southern England to forward base many of the fighter squadrons needed to support the landings. These used PSP or Marston Matting.
I'd recommend Robin Higham's "Bases of Air Strategy - Building Airfields for the RAF 1914-1945" for a review of the whole process of airfield building. This covers not only the U.K. but all the theatres of war where British forces required airfields.
And then add to that the separate question of airfield buildings, from control towers to hangars to accommodation blocks and specialist training buildings. For those see
Paul Francis "British Military Airfield Architecture - From Airships to the Jet Age"