A specialist sports store is probably your best bet. I think both Sweatshop (
www.sweatshop.co.uk) and Sweaty Betty (
www.sweatybetty.com) do stock F cup size sports bras so might be worth contacting your local store to check what they have in stock.
Both also offer sport bra fitting service also so it might be worth taking advantage of this while your there.
When your confident you know your sports bra size one other place you might want to look is TK Maxx. Takes a bit of a trawl but you can sometimes find a real bargain in your size even in those sizes which you can struggle to find on the high street normally.