one really does not generally have to pay income tax on winnings.especially day to day punters.
my brother is and has been a professional punter for 10years , t'over of millions p/annum and has a personal ruling no tax on winnings.
i guess this is because then one could claim losses as a deduction and the tax boys dont like that too much.

as already stated here you pay when you place the bet and it is a nice slug too.