Not true - there is an initiative in the UK started years ago to phase out checks, but it faced a lot of backlash and delays and is not anywhere on schedule. Checks are uncommon in the US as well, by the way, but you can see from the statistics I linked that cash and checks are still used in both countries.
The majority of, if not all, government benefits are paid directly to a bank account.
It is essentially impossible to live as a functioning adult without a bank account in 2016 in the UK.