I'm in Warlingham and they don't charge anything for delivery but I try to order at least 5 boards at a time, but I have suggested them to others who only wanted one board. You will have to pay the loose sheet rate which obviously covers the delivery & admin costs.
Oriented strand board / OSD / Sterlin Board is made up of flakes of timber pressed into a board, the surface is quite rough so it is only used for things like roof decks, sheathing under timber siding etc, definatly not paint quality.
Birch ply is a bit pricy but will give a good finish with a bit of work, you could also try MDF which give s a better paint finish and does not need to have the cut edges lipped.
The last time I was in a 'TimberCenter' they had blockboard on offer - it was a few months ago and I didn't see the price but I think they are nationwide now so maybe there is one near you.
Jason - on another tack - Birch Ply - are you able to get hold of better than B/B? If so can you let me know your supplier please - I basically want to leave it clear finished in some cabinets and I'm not sure B/B is good enough.