I have bought a product from Amazon and they tell me to contact the manufacturer.

If Amazon or any Internet Seller says that you must contact the Manufacturer over any faulty product, then you should advise them of your rights, and tell them that they are responsible.

Under the Consumer Rights Act 2015, Amazon or any Internet Seller is responsible for any faulty product and must repair or replace the item.
If they do not, then you have the right to take it further with Trading Standards.

You must also be aware that with any Internet Seller, including Amazon, you have 14 days to return any product whether faulty or not. This is at the sellers cost and responsibility and is under the Distant Selling Regulations (also part of the Consumer Rights Act), in which you are entitled to a full refund.

Many Internet Sellers, including Amazon do not want to take back product due to the high costs incurred, so they attempt to pass-the-buck to the manufacturer. It is their legal responsibility.

The manufacturer has no responsibility for faulty goods sold to the public via retailers or Internet Sellers. The manufacturer has a separate contract with these sellers.

Do not be offended if the manufacturer informs you to contact the seller!