Sale of Goods Act 1979. Supply of Goods and Services Act 1982. Sale and Supply of Goods Act 1994. The Sale and Supply of Goods to Consumers Regulations 2002.
• "It is the seller, not the manufacturer, who is responsible if goods do not conform to contract."
Your contract is with the sellar, in this case it appears that you have both the sellar and the Manufacturer eager to repair your phone.
From your point of view It really does not matter who repairs it, but question to ask if you get the sellar to do it will he use a third party.
If the manufacturer does it it should be as new.