Imperial College is not part of the University of London (it left in 2007).

In any case, the ‘University of London’ is an almost meaningless umbrella institution. Its members function as separate universities for all practical purposes.

It's not a part of the university of London anymore.

But this is semantics really, apparently the GP meant a very specific type of college but didn't communicate this and colleges that are universities under the hood aren't part of that unstated definition.