In 2022 at least, a whopping 6% of commuting trips were by bus and 9% were by rail. Even less for leisure: 3% of leisure trips are by bus, 3% by rail.
Hardly seems worth all the hassle.
https://www.gov.uk/government/statistics/transport-statistic...
Chart 4 is a summary of (domestic) travel modes and purposes.
In reality a big part of why people use cars is because there isn't a practical alternative, because we either haven’t built it, or we tore it down in the 70s/80s. There was a period where the UK government honestly thought that public transport was going to cease existing, and be replaced by private cars. The decades since have clearly demonstrated why that isn’t true, as usage of public transport has grown year-on-year despite chronic underfunding, and the slow dismantling of services.