I think the issue here lies with the company you purchased the phone from rather than o2.
Was there a warranty or guarantee when you bought the phone?
What were the terms and conditions of purchase for the refurbished device?
Goods need to be fit for the purpose but the company may have incorporated exclusions as to its liability given that it is a refurbished device.
Do you have the contract and any terms/conditions warranty or guarantee?
From the warranty link it would appear that you have a 1 year limited warranty.
From this document note this paragraph:
Any defect or non-conformity of goods with the contract which becomes apparent within 6 months of delivery are presumed to have existed at the time of delivery. After the expiry of this 6 month period, the burden to prove that the defect or non-conformity of goods with the contract existed on delivery generally shifts to the consumer.
When did you buy? When did you take the phone to the trader to report the fault?
If within 6 months then:
You may choose to have the phone either repaired or replaced free of charge.
Under statute it is a one attempt at repair. As this has been done you may be entitled to a replacement. It will depend on whether you reported the fault within 6 months.
Also note this:
It would seem reasonable for the phone to be replaced if ou reported the fault within 6 months of the date of purchase.
I hope this helps.
Unless you have any further details or questions please rate and accept my answer.
Ok so the six months have just expired. But by 2 days so you can still reasonably argue to a repair/replacement but you will have to prove that the goods were inherently faulty, i.e. show that there is no other cause, such as accidental damage, for the fault. To help you prove this, you may wish to obtain a second opinion.
If the seller does not help, you will need to write to them and make a more formal request. Say that you are exercising your rights under the Consumer Rights Act 2015 as the item is not of "satisfactory quality" and you would like to have it repaired or replaced. I would go for a replacement. In your letter, warn the seller that if it fails to accept to your demands you will start proceedings in the County Court.
Did you buy the phone with a credit card. If so, the credit card company will be jointly liable with the seller as the phone is not of satisfactory quality. You may then be entitled to a refund from your credit card provider under the Consumer Credit Act.
Do let me know if you have any further questions or queries. I would be happy to assist you further.
If not please can I ask you to take a moment to accept/rate my reply. Otherwise I will not get paid for the time I have taken to consider, research and type my reply. Thanks.