How old do you have to be to book a hotel in the UK?

I was expecting this post to be made by some 13 yr old girl who is meeting up with her 47 yr old 'boyfriend'.

To answer your question, different hotels have different age limits on occasion.

the exact first thing that came to my mind

I wouldn't expect any issues if you both appear to be 18 and have a credit card.

I have heard that some hotels/B&B's don't accept single sex parties due to stuff like hen or stag weekends ( and I don't blame them) but don't see how that now fits with anti gay legislation where a couple can be single sex.

But the point is that if one of you is an adult, considering that you could be married, there shouldn't be an issue unless they specify an age policy - - where they should tell you

It varies from hotel to hotel. Travelodge say:
You can only make a booking if you are 18 years old or over. If you arrive at the hotel and are under 18 years of age you will not be permitted to stay alone. We may require photo id as proof of age.
The fact that they say "you will not be permitted to stay alone" implies that you will be able to stay with someone 18 or over, though.
Hilton Hotels won't let you book online under 18 but say you can ring the hotel direct, perhaps because different Hilton hotels have different age rules.
You might need to search through all the "terms and conditions" small print of the hotel you booked at to make sure of their policy.

I booked a Double Trees by Hilton! Oh dear If I transfer the booking to his name, as he is over 18, will that work?

If you can do that it might save you worrying. The booking confirmation you should have been sent ought to tell you what documents you need in order to check in; often it's just the confirmation email they have sent, though some hotels do ask for ID such as a passport as well. Last time I used a Hilton Hotel (a few years ago) they wanted to take details of my credit card at check in, too, but they didn't ask for any other form of ID. I've found their telephone enquiry service very helpful so it might be worth giving them a ring to clarify things.

I'm sure you'll have a good time when you get there!

I want to book a hotel room for me and my girlfriend I am 15 so is she’s were both 16 next year I am 6ft though so would I be able to book a hotel room?