I'm not sure whether or not it counts as local, but Harringtons of Reading look like they deliver to GU14 (assuming I looked up the Farnborough post code correctly). The deposit is steep for the cylinder (~£80, refundable) but refils are £16.50 for 6.25kg and I receive excellent service. They also do propane/butane if you do AG on a gas stove. And they to wood for the log burner too
Alternatively, I believe there is a HBS in Farnborough - they may be able to recomend a supplier, if indeed they don't supply it themselves.
I use Harrington's - I got a quote from Pyramidsteel but the delivery cost was prohibitively high. As mentioned above Harrington's service is very good and delivery is only £5.