Business rates are charged for each day someone occupies a property on the rating list. If the owner stays in occupation and keeps control of your part of the space, the owner pays and may pass the cost on through your fee. If you are the occupier, tell the council's business rates team the date you start, and the date you leave, so the bill covers only your days.
Small business rate relief (opens in a new tab)
Check whether relief can reduce or remove the bill.