I have several friends at UCL, one friend at Andrews and i myself at Warwick. So i am in the best position to answer the question.
The academic difference between these 3 universities is negligible. Like my grandfather says, unless you go to Oxbridge no one gives an F.
What really matters is the city. They all 3 are so different. UCL is in London so that is self explanatory. St andrews is extremely rural. Warwick is very countryside like there's a campus bubble. But 30 minutes from both Coventry and leamington by bus. So halfway between Andrews and UCL's position.
The course also matters, look into the modules and see if they are right for you.