Hi Fortunata
All good advice above, just my bit (cannot put a value on it),
You mentioned that work has been carried out, therefore unless the BSC was after that, the BSC is worthless (was anyway)
The boat 'shows no sign of sinking' well paper boats float and show no signs until they do.
£500 for the survey is a big percentage of your £10,000 but it is a small percentage of the amount this boat could possibly cost.
Without seeing the boat etc. no one can tell you how much the overall cost will be but if needs re-fitting/plating etc. the cost could be as much as the original outlay.
Without knowing your circumstances, money availabl etc, but just look at what you could get for £20,000.
Will this boat be worth £20,000 (assuming that it needs £10,000 of work) when complete, to your needs.
Does the cost (£10,000) include a premium for the mooring and if so is the mooring definitely transferable [ask mooring owner, in writing].
Sorry to be pessimistic but pessimisum has saved me a lot of money.