There are two types of tax (of note here, obviously there are many other taxes too).
A service tax and Income tax.
In the USA all income is taxed which is why they have to declare winnings as monies earnt to the IRS.
In the UK winnings from prizes or gambling or not classed as earnings and not declared as income for amateurs. (Although once they become an asset earning interest this is taxed like any other savings).
If gambling is the primary source of income, then this is a professional status and the income would be declared, but also some expenses can be offset.
The Service Tax is normally applied at source collected and paid by the service provider (like VAT).
But when the service provider is registered offshore they manage to avoid it.
This is why France
and other countries now have to use locally registered poker sites so the rake can have gambling tax added. Which the UK (Bastids) have noticed and are now considering.
So in short, at the moment you don't have to worry about any tax on poker as a UK player.