I think it's going to be a bit overblown. It's easier for EU tech employees to move their lives, than it is for London tech companies to up and move elsewhere. Because of this, I theorise that there will be an intermittent period where there will be a labor shortage in London, due to lack of EU workers to supplement the demand in London tech. This will balance out with time, with EU companies moving more of their offices out of London.
I think we have started to see this already, at my gig, we have found it quite difficult to get decent candidates through the door, and anecdotally a lot of our better candidates have been from the EU. We are about 50% Londoners, 30% EU, 20% World.