The British invented the concept of the resonant cavity magnetron which enabled very compact, high frequency (centimetric) radar to be developed. However, we had no resources to develop the idea at the time so it was transferred to the US (specifically the USN) who developed the VT fuze.
The Germans never developed centimetric radar in time, but they did try other ways of achieving the proximity effect, e.g. by using a light meter which would show a drop in light levels close to the target.
Tony Williams
New book: Rapid Fire - The Development of Automatic Cannon, Heavy Machine Guns and their Ammunition for Armies, Navies and Air Forces.
Details on my military gun and ammunition website:
http://www.users.globalnet.co.uk/~autogun/