There are way more than three networks in the UK, but BT, TalkTalk and Virgin Media are by some measures the most popular and broad in reach... Vodafone and Sky are two other common ISPs that have unbundled the local loop in the same way as TalkTalk (i.e. they have equipment in BT exchanges so that no BT backhaul is needed).

See https://availability.samknows.com/broadband/ for what is available in your area (may not include other mobile, satellite, fibre providers)