Non payment of rent is one of several grounds for eviction in section 8 of the 1988 Housing Act.
Your first action should be to check that your tenant is actually in residence. You may not enter the property without the tenants permission, so if you suspect the tenant has left, you need to follow the abandonment process.
As soon as the tenant has 2 FULL months* unpaid, you can serve them with a section 8 notice under grounds 8, 10 & 11. 14 days later, you can apply to the court for a possession order using the Possession Claim Online website.
It will take around a month before the hearing takes place, but so long as there is still 2 months unpaid, you will get a guaranteed possession order under ground 8. If some rent has been paid, the judge can consider giving you a possession order under grounds 10 or 11. The judge can order the tenant to repay the missing rent too.
If the judge grants a possession order, the tenant will be given at least 14 days to go. If the tenant still refuses to go, you will have to employ court bailiffs, which is more expense and time.
You should also look at the section 21 process, but s8 is usually the quickest option.
DO NOT be tempted to use any process other than shown above. to do so will almost certainly be illegal eviction, which is a criminal offence.
* 2 months relates to monthly paid tenancies