London banking future after brexit

They shouldn't. If they throw a temper tantrum and move offices outside of the EU they will only be hurting themselves.

As per Armstrong:

The markets will settle down and then flip. The smart money will figure out that London will remain as a financial center, as will Zurich. But there will be no such center within the EU because the politicians have a mechanism in place to outlaw short-selling at their discretion whenever the markets say they are wrong. BREXIT is the survival of Britain, not its demise. The crisis brewing is eight member states will ultimately follow Britain and hold referendums.

He's not wrong. If you've been watching the markets for the past few years then you would know that the EU has been aggressively cracking down on the movement of money within the EU, even to the point to where they are trying to figure out how to outlaw both cash and short-selling. You would also have noticed that there have been massive capital outflows from Europe to the USA.....THAT is why stock market valuations are so high. It has nothing to do with "fair value" or investors anticipating growth. It's money trying to escape the conditions in the EU by one of the few means that isn't blocked by "money laundering" laws.

By moving outside the EU, the UK stands to benefit from capital fleeing the EU....and large capital inflows, should the UK transition and manage it well, will mean that London investment banks will have a good time.