The Sales of Goods Act does not apply to contract mobile phone suppliers. It's the Supply of Goods and Services Act which applies:
"If you get goods with the service, the same rules apply
When you buy goods on their own, with no service attached, you're protected by the Sales of Goods Act. Yet if you buy goods as part of a service, eg, a handset with a mobile contract or a boiler that you ask a gas company to fit, you're protected by the Supply of Goods and Services Act.
And if the goods supplied as part of the service become faulty, it's the service provider that's responsible for sorting the problems, not the supplier of the goods.
The protection's the same as the Sale of Goods Act, though - in short, the Sad Fart rights. It's just that complaints must be made under the service law instead." Money Saving Expert
The mobile phone supplier is within their rights to insist that the phone is sent to the service provider for remedy. They are also allowed to repair the product rather than replace it.
All that leaves is the battery, which needs to be sorted quickly.