Right, lets look at basics here. Assume the rent is paid monthly in this example. The tenancy started on 8th, thus each period ends at 23.59 on 7th (It is highly unusual in property contracts for it to expire at a set time during a day).
Keys are a key factor here (no pun intended). The act of parting with keys is a physical act recognised in law as parting with possession. If keys are held, possession is retained. Thus in your example they still had possession on the 8th. If they had given written notice that they were leaving on 7th and didn't, their notice would have expired as it was not adhered to. They would again need to give written notice of a new date.
As they have possession after the start of a new period in their tenancy, the Protection from Eviction Act 1977 comes into play. This states (clarified by case law) that a tenant has to give written notice at least four weeks before the end of a period of their tenancy. It follows that rent is due for the whole of that period, and thus they are liable for a whole month's rent, not just one day. It gets worse for a tenant though if they don't give written notice. In Laine -v- Cadwallader (2000) 33 HLR 397 written notice was not given so the landlord was successful in obtaining rent to the end of the period and four weeks beyond.
I see no reason why Cadwallader and the Distress Act can't be combined, making double rent payable for the whole period the tenant is liable for.
Of course, we, like most landlords I hope, would use commonsense. Particularly for the majority of decent tenants. In your example above, I do play with the tenants a bit and tell them the law, but I would only charge a daily rate. However, if the tenants had been snotty and a pain in the 4rse then I do use the law as written.
David
Long ago, below an picture of a 4-masted sailing ship in a heavy storm was added: "A ship in a harbour is safe, but that's not what a ship is designed for"