Ouch. That would make a dent in the bank account. I also don't associate a black LP with Clapton. Yes, the sunburst LP during the Bluesbreakers time, a 335 or SG with Cream and then obviously a black strat.
A quick Google does pull up a handful of photos, but I certainly wouldn't associate this with him specifically.
And £17500 when you could get pretty much 10 Clapton signature strats...? No thanks. Although, I suppose that is cheaper than an original 1958 one.
You can buy a new (non signature) one for about £6000. So a 'signature' is worth over £10,000?