Back in September the DVSA announced they would be stopping tests for car drivers towing a trailer so they could free up slots for other types of tests (such as HGV). A law needed to be passed (which did so yesterday) allowing all full licence holders to be able to tow without taking a further test. This has raised road safety concerns and it is advised that anyone looking to tow for the first time does undertake some training, although the accreditation scheme will not be in place until next year. If you are a provisional licence holder, you cannot tow.
If you passed your driving test from 1st January 1997, you can now tow trailers up to 3,500kg maximum authorised mass (MAM). If you passed your test before this date, you can tow a vehicle and trailers with a combined weight of up to 8,250kg.
On photocard licence renewal, the DVLA will automatically add the category B+E to the licence of all drivers who passed since 1st January 1997 and all new licences issued. If you want to check if you have the B+E category, you can do so here.
There is a page on the gov.uk website which explains what you need to do to be towing safely.
Make sure you are aware of the laws around towing, such as different speed limits. You can find out more in The Highway Code.