Couldn't you bootstrap it, get £5k on a credit card for the taxes to exercise some of the options, use the profit to pay the taxes on the rest (or a further bootstrap)?
But the Revenue consider you to have received value in that "piece of paper" that you can't liquidate? That just seems like perverse tax law - why is it that way?
Surely if they're private shares that can't be sold the extrinsic value is zero, the private share value for tax purposes is no greater than the value of the option?