Then that is a problem for you. If it is out of warranty they are under no obligation to repair.
However, I will outline the process to seek for them to do so, in the event you want to try anyway.
You need to write and set out your losses and request they repair or a refund of the repair cost (£6000) within 14 days of the letter of claim, or say you will go to Court within 14 days. You should make sure you send this signed delivery and keep a copy.
If they do not then you can issue proceedings in the County Court. You can either do this online at: www.moneyclaim.gov.uk or by completing form N1 https://www.gov.uk/government/publications/form-n1-claim-form-cpr-part-7
and take it to your local County Court.
The Court will then issue a claim which a copy will be sent to the Defendant who will have a limited time to defend it, if not you can enter Judgment and enforce.
If the claim is for £10,000 or less it will be a small claim so you will not need legal representation. Over this value you would need representation for trial.
Can I clarify anything for you about this today please?
If not I would appreciate a 5 star rating for my answer, the button should be at the top of the screen. If you need more help, you can ask follow up questions for free and I would be delighted to assist. Thanks!