Tenant Leaving UK with Rent Arrears: What to Do

My tenant said he's leaving the country next week, but he still owes me thousands of pounds of rent after deducting the deposit. I gave him two months' notice to leave, and the date to go is 24th May. But he said he has nowhere to go between the day he leaves the country on 29th May. What should I do to recover the unpaid rent and hold him accountable for any loss that I have due to his illegal stay?

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Preventing, Controlling and Recovering Rent Arrears

The tenant's responsibility is to make sure rent is paid in full, on time and in the manner agreed in the tenancy agreement.