I had this with a guy before xmas, Could understand if it was bald tyres, no brakes or something.
But I think thats why you can have upto 1 month of existing test added to your new certificate, to stop people waiting til it expires.
Heres a quote taken from another forum I use
No your current Mot remains valid,you could get prosecuted under the construction and use act though if your car is defective, but there again you could get prosecuted a day after a new Mot was issued if the car is faulty!