London and Bruges are so different that they are impossible to compare. It is a bit like comparing New York City and, say, Carmel in California.

Bruges is a cute, twee, chocolate-boxy kind of town. Personally this just is not my cup of tea at all (As some have suggested, I would rather go for Ghent which is rather less artificial and touristy) but a lot of people love it so it really depends of what your tastes are.

London is a major European capital which has infinitely more to offer than Bruges. But that, in itself, may be a weakness if your trip is only 8 days long and you are trying to fit a visit to Paris and Amsterdam in that time. The fact that Bruges is a small place whose charms are relatively quickly exhausted is probably an advantage from that perspective.

It seems to me that trying to fit London, Paris and Amsterdam all in an 8 days trip is too ambitious and, for that reason, I would go for Bruges (or rather Ghent personally ) over London If I were in your shoes. Also, as others have said, from a logistics point of view, Flanders fits ideally in between a visit to Paris and one to Amsterdam.