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Lodgers, under UK law, don't have the same rights as a tenant would. As a result once you've given them 'reasonable notice' they have no right to stay in your property. However, if you want to evict a lodger who refuses to leave you'll need a court order.
In order to minimise the chances of any disputes occuring in the first place it's highly advisable to have some form of written agreement between you and your lodger. This can detail any conditions you want to impose in addition to setting out in clear language what each of you can reasonably expect. This can also contain a notice period for both you and the lodger if desired so you both have a little warning should the other party decide they want to move on.
Lawpack have contracts and agreements available for download.
If you don't have a contract then you need to give your lodger 'reasonable notice'. This doesn't need to be the 28 days which is standard for many tenancy agreements but should give them a chance to find somewhere else.
We'd recommend you give notice in writing as well as verbally just to cover yourself. Even if you get on well with your lodger you should take this precaution (you can explain that's all it is) so you both have a record in case of any dispute at a later point.