How can I find the tall, dark, handsome man who approached me in the British Library cafe last Wednesday?

You’ve described me very well but alas I was not there at the time in question. Go in at the same time on the same day of the week and see if this accidental encounter happens again.

you could try craigslist missed connections

If it’s meant to be, he’ll come in and find you again. Do you work there?

Go and hang out at the British Library café on Wednesdays see if he comes back.

The Metro newspaper has an ad column for just this sort of thing. Put your ad in there, maybe he reads the metro on his commute.