No. It's the retailer's responsibility to give you your money back. From s14 of the Sale of Goods Act 1979:
(2) Where the seller sells goods in the course of a business, there is an implied term that the goods supplied under the contract are of
satisfactory quality.
(2A) For the purposes of this Act, goods are of satisfactory quality if
they meet the standard that a reasonable person would regard as
satisfactory, taking account of any description of the goods, the
price (if relevant) and all the other relevant circumstances.
(2B) For the purposes of this Act, the quality of goods includes their
state and condition and the following (among others) are in
appropriate cases aspects of the quality of goods—
(a) fitness for all the purposes for which goods of the kind in
question are commonly supplied,
(b) appearance and finish,
(c) freedom from minor defects,
(d) safety, and
(e) durability.
If your goods are faulty after a month and a half, it would appear that the goods are not of satisfactory quality as they lack durability - s14(2B)(e) above.
The Sale of Goods act is very clear that your contract is with the seller. You have the right to terminate that contract, because s14 is always a condition if you're a consumer. Furthermore, the seller cannot exclude liability for breach of any terms regarding the quality of goods, and specifically, they can't exclude themselves from liability under s14 of the Sale of Goods Act. All of this is found in the Unfair Contract Terms Act 1977.
So the answer is: you appear to have a reasonable case for returning the goods to the retailer, and they are required, by law, to give you their money back. If you sent the goods back to the manufacturer, those rights shouldn't be affected, on the basis that UCTA states that those rights cannot be excluded.
(Disclaimer: this shouldn't be taken as legal advice, merely advice given peer to peer. In your situation, that's what I would argue myself.)