If a tenant gives you a notice to quit, they should leave on the date they have specified in the notice. If they fail to leave on that date without your permission, then it is possible to charge them double the rent that was due before the notice date expired. [s.18 Distress for Rent Act 1737].
This article explains the procedure for claiming double rent and for seeking possession when a tenant has given notice but failed to vacate. See also our court forms possession procedure guidance page for details on seeking possession if a tenant fails to vacate after they have given notice.
s 18 Tenants holding after the time they notify for quitting, to pay double rent.
And whereas great inconveniences have happened and may happen to landlords whose tenants have power to determine their leases, by giving notice to quit the premisses by them holden, and yet refusing to deliver up the possession when the landlord hath agreed with another tenant for the same: from and after the said twenty fourth day of June one thousand seven hundred and thirty eight, in case any tenant or tenants shall give notice of his, her, or their intention to quit the premisses by him, her, or them holden, at a time mentioned in such notice, and shall not accordingly deliver up the possession thereof at the time in such notice contained, that then the said tenant or tenants, his, her, or their executors or administrators, shall from thenceforward pay to the landlord or landlords, lessor or lessors, double the rent or sum which he, she, or they should otherwise have paid, to be levied, sued for, and recovered at the same times and in the same manner as the single rent or sum, before the giving such notice, could be levied, sued for, or recovered; and such double rent or sum shall continue to be paid during all the time such tenant or tenants shall continue in possession as aforesaid.