It's more likely to be the other way around. People will still try to migrate from the EU to the UK - as they are already doing in huge numbers and are still doing years after the Brexit vote. If there was going to be a major drop in immigration numbers it'd have happened already and it hasn't. In fact immigration from outside the EU has gone
up not down.
The amount of fearmongering going on around this topic is quite eye opening and can only mean opportunities for people who keep their head. The top voted comment in this thread is saying that euro clearing moving out of London will "kill the market" and "be a shot in the head".
That person clearly has no idea of the size of the euro clearing market (small), or the fact that it will hurt the EU significantly more - that activity not only takes place in London for good reasons, but it exposes the UK to significant risks in case of clearing house failure ... not an entirely unthinkable problem given the eurozone's dire economic straits (stalling despite negative rates). I'm OK with it though: short term loss of relatively minor profits for banks is probably worth the insulation from the threat of government-backed bailouts in case of eurozone problems.
Also note the article: that money is leaving the UK because the EU is forcing it to leave via regulation. That's not a good sign for the strength of the EU economy - they can't win their own banking business on their own merits and have to literally ban Europeans from using British services to stop them doing it.
My view is simple - the EU is heading in the wrong direction, fast, and not even attempting to turn around. There's a train wreck coming for sure but it's not coming to the UK, as long as we get out in time.