The UK government has demonstrated a willingness to help the UK's tech sector get the talent it needs from outside the EU by streamlining the process for getting Tier 1 visas. Even if movement of labour is restricted after Brexit, I expect there to be a huge difference in the restrictions applied to unskilled migrants versus skilled migrants. In short, I don't think UK companies need to worry about being able to bring in the sort of talent they need.

The fate of London's financial sector will depend on what sort of trade deal the UK and EU negotiate. The worst case scenario would be if the UK was denied access to the single market for financial services, including "passporting". However, the UK imports a lot more from the EU than it exports[1], so countries like Germany and the Netherlands are likely to accept a deal which means London continues as Europe's financial capital, in order to protect their own economies.

1: https://twitter.com/JackGavigan/status/747338413754331136