Don't really know much about 13 yo boys but might he be a bit old?? I mean my dd who is 4 can't get enough of the place. But then your ds might be really into animals. Dh's godson is 16 and still likes the place but - much as I love him - he is a geek.
The animals are well looked after and seem pretty happy. No cages. The gorilla kingdom, in particular, is amazing.
Also it's not that big so you could be done in a couple of hours.
And at half term it will be mobbed - get there early if you can.
The Imperial War Museum is v v well-regarded by lots of parents of boys I know, if that helps (have never been there myself).
Went last summer and have to say was disappointed - no elephants and lots of enclosures were seemingly closed. However, the gorilla kingdom and the butterfly house (which I think was temporary) were fab. If you like birds then it's the business but otherwise I wouldn't go back
What about the Transport Museum? It would be cheaper as you only pay for an adult and kids are free. Yuo don't have to be really into trains to like it. There is lots of interactive stuff to do. My eldest is only 7, but I have been with a family that has older boys and they liked it. It will be busy during half term, but so will everywhere.
my son aged 9 loved the imperial war museum. we have been twice and it is fab. There is a anderson shelter you can go in and a submarine as well as a great exhibition about being a child during the 2nd ww. As far as zoos go. We prefer Colchester zoo to London Zoo
I like it but I live near - and not sure about 13 year old. As well as IWM, if your DS is interested in things like that, may I also suggest RAF museum at Hendon? It's free to get in, loads of planes and not that busy. And for someone who has no more than a passing interest in aviation, I really enjoyed it!