Boer,
as well as endorsing the advice given on looking at the GB F-Class Association website (and look specifically at the F/TR section which is what you'd be shooting in with a .308W)
http://www.freewebs.com/fclassuk/ftronly.htm
I'd suggest you speak to Stuart Anselm of Osprey Rifles in Oldham Gtr Manchester
http://www.ospreyrifles.com/
Stuart is the GB F/TR team captain, a very successful F/TR shooter in his own right and has built many successful rifles in this category at reasonable prices. Stuart mostly uses the Savage PT single-shot target action.
Another northern F/TR rifle supplier mostly using New Zealand Barnard actions is Brian Fox in Stockport, Gtr Manchester who has a part-time shop on Diggle Ranges.
http://www.foxfirearmsuk.com/
Both supply specialist lightweight wide-angle bi-pods too for F/TR class shooting. Between them they account for the majority of recent UK F/TR rifle new build.
As you're obviously close to Bisley given the original post, there is a GB-FCA training weekend taking place next weekend 19-20th Feb. Contact Mik Maksimovich, the associations' chairman (Mik also builds F-Class rifles being one of the two guys behind Dolphin Arms), re having a chance to watch and talk to some of the F/TR shooters in one of the on-range sessions. Stuart Anselm may well be there too.
Finally, if you haven't found it already you ought to be reading the UK's free online target shooting magazine
http://www.targetshooter.co.uk/
which has had several features on F/TR rifles (including two of mine) as well as F-Class (Open that is) rifle builds. It has a monthly F-Class report ("The Long View") on GB-FCA rounds and matters. Old issues are available as PDF files in the Archive section.
Don't be put off by all the mention of national rounds and the national body if you plan to compete at club level only. These people will help you with advice on getting up and started at any level. Association membership is cheap (£15) if you want to join, and if you have good access to Bisley, there are two national rounds held there this year, the Long-Range meeting (1,000-1,200yd) on 2nd/3rd July and the F-Class European Championship meeting (4th-6th November, the third day for team shoots only).
Laurie,
York