How to interpret this Cambridge, Blackheath here?

I’d like to ask about the following sentence from The Missing Three Quarter by Conan Doyle.

I didn’t think there was a soul in England who didn’t know Godfrey Staunton, the crack three-quarter, Cambridge, Blackheath, and five Internationals.

This Godfrey Staunton is at the moment belongs to the rugby team at Cambridge University. So what the word Blackheath refers to here? I don’t think the relation between these words, Cambridge and Blackheath, is like “Los Angels, California”. If it’s not “Cambridge in (/ of) Blackheath”, I’m guessing Blackheath is the name of high school Godfrey went to. So this part means as “Godfrey Staunton was an excellent three-quarter back at Blackheath high school and he is now an excellent three-quarter back at Cambridge University.” Am I right? Can someone tell me? Thanks.

Solution 1:

No, Blackheath is a district in London. (https://en.m.wikipedia.org/wiki/Blackheath,_London)

This is just a narration that says that Godfrey was popular at Cambridge University, moreover, in his district, Blackheath, and actually was a star of five Internationals.