There are two issues here - can they book the hotel, and can they stay in it once booked.
The answer to the first, under UK law, is that they cannot enter into a legally enforceable contract to book the hotel - so many hotels or operators will not accept their booking because they have no come back if things go wrong.
Can they stay in it, one booked - it's up to the hotel, not really a matter of law. Some allow it, some don't. Some that don't on paper may not enquire too closely in practice.
And abroad is a big place - there may well be countries that have laws against 17 year olds travelling unaccompanied. I don't know of any off-hand though.