Regarding rejection, sometimes customers suddenly realise that they cannot afford the car on finance and look for an easy way out. Now this does go on and sometimes a dealer has to see if this is the case. Regarding time periods, this is unclear, but certainly a year is a reasonable time to allow a dealer to rectify faults that have occurred repeatedly. Note the wording repeatedly. If a vehicle has several different faults this is quite a different matter to one repeated fault that cannot be rectified.
Most dealers will try and come to a compromise, even if the faults or circumstances are not legally capable of rejection. A happy customer is better than an unhappy customer, and an unhappy customer generates more publicity! An exchange of vehicle, with a similar mileage or specification, may be satisfactory, this is voluntary from the dealer and not a legal requirement.
Also dont expect the earth, I know of one customer at another dealer who wants to reject a vehicle of 25k miles, nearly two years old and will only accept a vehicle costing 7000 pounds above the new price of his vehicle as an exchange. Dream on.
I still say negotiation is the way to proceed as far as possible.