You know if a betting site is legit by their gambling licence. The United Kingdom Gambling Commission is the governing body on UK online gambling, and it hands out licences to those sites that meet specific requirements.
If an online betting site has a UKGC licence, you know they have met the requirements that UKGC places upon them and shown they can be trusted to provide gambling services within the UK.
Even though this is not the 100% guaranteed way of looking if a site is legit, it is an easy way to get very, very close. Those sites who have a UKGC licence and are not legit are extremely rare and will be punished and heavily fined as soon it becomes known.