I had a 3-part cashback deal with Carphone Warehouse and like most people, the 1st was withheld/lost/wrongly applied for; but they paid up the 2nd and 3rd with no problems amazingly. After going through a long (and correct) course of action - telephone, letter to customer service, letter to executive office, final letter) - I had to go to small claims court to recoup this cashback. I was advised by a lawyer friend of mine that it is a clear-cut case for the consumer as long as they follow the instructions and try everything possible before applying for the court to intervene. I've not heard of one incident where CPW won over the consumer, although I have heard of someone who didn't write any letters and was told to go and try that before applying for legal proceedings.
If you send the correct bill in by recorded delivery within the time limit, then they are legally obliged to pay you. If you do send in the wrong bill in, they have an obligation to tell you asap so that you can rectify the situation. If they fail to keep their end of the cashback/chequeback deal within your contract, they are in 'breach of contract' amongst other things.
I should add that if you have subsequent costs after you send in your court claim, you must request that the amount to be reimbursed be changed through the proper forms. The court won't award an 'x' amount for extra costs, only what you have claimed they owe.
EDITED:
My claim was with E2SAVE too but since they are owned by CPW and Andrew Heddle (MD of E2SAVE) was useless at dealing with my problem, I ended up approahing Charles Dunstone (MD at CPW) to sort it out. He didn't/couldn't be bothered either so I had to start legal action against E2SAVE as they were who I agreed my contract with.