@Gargron having moved to London 12 years ago, I can report that the visa situation is daunting, difficult and extremely stressful. But London is great! My big tip is: do whatever you have to to limit the time the Home Office has your documents. Periodically there are still reports of things like this from 2018. https://www.theguardian.com/uk-news/2018/may/31/vital-immigration-papers-lost-by-uk-home-office?CMP=Share_iOSApp_Other