You will only be entitled to bring court proceedings to evict your tenant if you have served the proper possession notice first and waited until the notice period has expired. (There are a few exceptions but these are rare).
Note that it is a criminal offence to evict a tenant other than by obtaining a court order for possession in the County Court, and then (if the tenant still fails to vacate) by using the County Court bailiffs. Even asking them to leave if you have not followed the proper procedure can be considered harassment.
It is important that possession notices are correctly drafted and the correct notice period is given. Otherwise, they could be invalid and you could lose your possession claim at court.
You need to be able to prove to the court that your notice has been served. Keep a copy and serve by hand. If you think the tenant will deny receiving the notice, take an independent witness with you.
The quickest and cheapest way to evict tenants is by using the ‘accelerated’ procedure, which is based on a previously served section 21 notice (which must give at least 2 months notice and which cannot expire before the end of the fixed term). In accelerated proceedings, the Judge makes the order on the paperwork provided and there is normally no court hearing. However, despite being called ‘accelerated’ it is not particularly quick. It will normally take between 8 to 12 weeks before an order is obtained. Note that it can ONLY be used for assured shorthold tenancies.
If you wish to evict because of your tenants’ bad behaviour, you are advised not to use any of the ‘discretionary’ grounds for possession save in exceptionally serious cases. Because the tenant can put in a defence, these cases generally become long drawn out and expensive (particularly if your tenant obtains legal aid to defend). It virtually all cases it will be quicker and cheaper to wait and use the accelerated procedure.
If your tenant is looking to be re-housed by the local authority, note that they will not normally do this until a possession order has been made against the tenant, and sometimes not until a bailiffs appointment has been made.
Depriving someone of their home is a very serious matter, so Judges will expect landlords to follow the proper procedure, have perfect paperwork, and are generally unforgiving if mistakes are made. Note that if a landlord loses his claim he may be ordered to pay his tenants legal costs. This could prove very expensive if the tenant had legal aid. So be VERY CAREFUL make try not to make any mistakes!