Legalities of ending a tenancy?

I want to move house and i am currently renting, and want to move to another house to rent, but the estate agents have told me that i have to move in one day an they wont give me the keys until the day that my other tenancy ends as they said it is illegal. ive done this before (overlapped on renting) on every other house ive had when i just go in to have a little clean up etc and i dont see how they expect me to move, clean up, meet my old landlord to inspect, meet them to inspect new house, collect new keys, sign iventorys an contracts all in one day its ridiculous! surely it isnt illegal to just keep the property on for cleaning, my other landlord said it was utter rubbish! Help!