Hi,
He had first picked her up in London, at one of his richer friend's.
Here's yet another way to look at it.
We have the adjectives rich, richer, richest. We can use these to divide our friends into groups. However, there is no reason why we always have to divide them into 3 groups. If we wish, we can just divide them into 2 groups. We can just say This group is richer than this group. So, this person is from the group that contains my richer friends. He/she is one of my richer friends.
I also have an additional point. One of must be followed by a plural, which in this case is friends. This means that the apostrophe should be written for a plural noun, ie
He had first picked her up in London, at one of his richer friends'. (meaning one of his richer friends' homes)
Best wishes, Clive