I have some questions as they relate to some grammar.

By the time Alex finished his studies, he had been in London for over eight years. OK

Now I know that this sentence is in the Past Perfect but I also know that many times we can arrange sentences differently.
Here is another sentence but it has been rearranged.

Alex will have been in London for over eight years by the time he finished his studies.

'Alex will have been' is Future Perfect. You can think of this as 'the past in the future'. Let me offer a simple example.

I will arrive in London on June 1. I will leave London on June 11.

By the time I leave London, I will have been in London for 10 days.

Thus, if you are talking about 'the past in the future', your sentence above needs to be

Alex will have been in London for over eight years by the time he finishes his studies.

On the other hand, if you are talking about the actual past, you'd simply say  it as you did in your very first example above.

This sentence contains the grammar necessary but appears incorrect to me.  When the expression

by the time

is used, this second sentence appears incorrect but if I write the same sentence slightly different using the word

before subtituting by the time the sentence seems to be correct.

i.e. Alex will have been in London for over eight years before he finished his studies.

My earlier comments still apply, whether you say 'by the time' or 'before'. 

Best wishes, Clive