This is my understanding of it.

When selling your bitcoins in the UK you pay capital gains tax on the profit.  If you're a basic rate tax payer (i.e. you earn less than £45,000 per year), then you pay 10% CGT.

Example:

You buy 10 Bitcoins for £5 each many years ago.

You then sell 3 of these Bitcoins for £45,000.

You then deduct the cost of the Bitcoins £45,000 - £15 = £44985

You're allowed £11,300 tax free, so 44985 - £11,300 = £33685

You pay 10% tax on £33685 = £3368.50 tax.

Theoretically, if you had a partner who you trust and also is a basic rate tax payer, then they could also sell the above amount and pay 10% CGT.

In total you could sell around £90,000 per year between you both and pay 10% tax.  If you're patient enough do this every year, rather than selling all at once.

I'm happy to be corrected if anyone now differently.