OP, some of the advice here is right and some of it is wrong. It's a bit more complicated than 'a lodger must leave whenever told so' but just for the record I wouldn't have him back either.
Generally speaking a lodger is entitled to reasonable packing up time, as they are a licensee not a tenant. Reasonable is not however defined by law. Some people's take on this is a few days, some people's take is one rent period (as in, if you receive monthly rent, give a month, weekly a week, etc).
Where people get into difficulty is if the lodger has a fixed term, then you can't actually end it early without a breach of the agreement- please put in clauses in future agreements to cover things like missed rent, damage to property, antisocial behaviour and anything else you couldn't live with.
If you have a contract that states a notice period, you are technically bound by that. However, I sincerely doubt this man will take a case against you. Realistically he's got bigger fish to fry, and what kind of remedy would he even ask a judge for? He'll not be reinstated and given he is behind on rent he has no financial loss. You can't be prosecuted for illegal eviction like a landlord/tenant arrangement.
The police have tried to make this your problem as he'll have bail conditions and if he has no suitable address he will have to be recalled or will have to sort something.
What a shock to get in the middle of the night, intricacies of the law aside, stand firm and consider changing your locks.