Essentially, none. There are three common spiders in the UK that are capable of biting you: the cellar spider, the woodlouse spider and the false widow spider. Their bites are painful and have been known to cause swelling for a few hours.
In 2014 a 60-year-old woman died after being bitten by a false widow spider. However, the cause of death was due to a bacterial infection from the puncture wound, rather than the spider venom itself.