No. they can't do this to you.
Sit yourself down, take a deep breath and compose a letter to them that states the date you gave your notice, the original date that you were leaving.
Then detail that you were called on such and such a date to advise you that they had found a new tenant that wanted to move in asap and therefore could you move out earlier.
State then 'At great inconvenience, we managed to accommodate the date you informed us of and have been working to that date until yesterday.
We have arranged for final bills until that date, standing orders, insurances and direct debits cancelled, re-directed our post, arranged for help to move, arranged for transport etc etc all to accommodate the date that you insisted upon.
Now, less than 4 days before we are due to move out, you tell us that we have to pay for another week, for the property we will no longer be living in having been ASKED to leave on that earlier date set by YOU and the landlord.
This request is highly irregular and utterly unreasonable. We will be leaving as requested. If the new tenants are delaying their move in date, then they need to cover that week, not us.
This is just my gut reaction, Get some CAB advice on this pronto though!