I moved to London to do a startup in December 2019. All I can say is do not do this. The government during covid has been horribly inefficient, I just received my NHS ID in the last month (taking upwards of a year to process, during which time they denied me covid testing after I had the necessary symptoms) and I received my NINO 6 months after moving here, however now with covid they aren't even processing these anymore.

In terms of brexit, any sort of gains for a startup will be possible only if the British government allows them to be (for example with deregulation or the removal of GDPR or the reduction/easing of bureaucratic proceses). In my experience betting on the British government to do the right thing is a bad bet. They have the digital London effort but it seems more like a PR stunt than a good-willed effort to attract startups.

You will also encounter strange socio-economic effects that you would not see in other places, for example being an engineer and starting a startup here is viewed as a negative while being a business major is a positive. There is a big divide between capital and labour that perpetuates itself through these stereotypes that are not present in places like America.