I would not see that provision as being unfair. Normally there are several options, fully flexible with a right to cancel up to the day of arrival and fully paid at a lower price with no cancellation right. If the "second wave" arrives in time and the hotel is closed, you would then have a right to a refund.

It seems by paying in full upfront I have no right to cancel. I think the contact term used is unfair and makes the contract unenforceable in law. Does anyone agree?

I'm not sure that I do. Pay in full at booking, no cancellations or changes, is a common condition for advance bookings and usually secures the deepest discount. Most of the chains like Premier Inn, Travelodge or Accor will offer a more flexible arrangement for a modest increase in cost.

October is still some four/five months away (depending on which end of the month the booking is). It's too far out to know yet whether some or all of the activities you mention will be available or in some restricted format. If I was guessing I'd say sightseeing is possible even now, as is some limited shopping with further easing promised. Theatre is the most likely casualty.

If by, say, 3 weeks before your visit it still looks as though London is in total lockdown with second, third or subsequent wave it might be different.

Try these guys for a professional opinion:

https://www.citizensadvice.org.uk/consumer/get-more-help/if-you-need-more-help-about-a-consumer-issue/

"All I have is a copy of my reservation with this statement -- A credit or debit card is required to charge full pre-payment at the time of booking. This is non refundable and cannot be modified in the event of a cancellation

It seems by paying in full upfront I have no right to cancel. I think the contact term used is unfair and makes the contract unenforceable in law. Does anyone agree?"

It seems to me to be a straightforward issue of contract law. You have entered into a contract with the hotel and as part of this have paid for a service that the hotel has agreed to provide. Unless the hotel cannot or will not provide the service, you have no right to expect a refund on the basis that you don't fancy travelling. Even if you were ill and physically unable to travel you have no right to expect a refund - though in that situation you could appeal to the hotel management's compassionate side.

Certainly contracts need to be fair and reasonable and it's remotely possible a lawyer might be prepared to argue in court about this - at (your) considerable expense, of course. But common sense suggests it's not unreasonable. You knew what you were getting into and were not deceived or coerced.

As others have suggested, your best bet is to sit tight and see what happens. If the hotel is closed for the dates of your booking you can then demand your refund.

Have you contacted the hotel and asked whether you could get your deposit back? Given the current climate, I would hope that they would be more understanding when it comes to cancellations.

Any luck gramar?