Do I really have to give 4 weeks notice?

m paid weekly. I have given a week and 2 days notice that I wish to leave the company. When I originally started with the company the contract was for 4 weeks notice but this company has now been taken over and the original company now no longer exists. I have never been given a new contract by the new company. Do I really have to work 4 weeks? - I do not think this should be the case as having worked for the week I have given notice for what is the incentive to work for a further 3 weeks? - please advise