Didn't freddietheca mean H-H-Hancock's Half Hour?! But I don't recall it as the theme to anything. It was certainly requested on radio a lot. Most likely to have been used in comedy movies few times.
The theme from The Men from the Ministry (BBC Radio) is called Top Dog (by Ivor Slaney) and is available on a CD, with many other similar pieces, called "British Light Miniatures - Vintage TV & Radio Classics" which can be bought from Amazon etc. and also as an MP3 download from them.