If somebody does work for someone else, provides a service, or supplies goods, and does so as a business to a consumer, then under the Consumer Rights Act 2015 the:
Goods must be as described
Of satisfactory quality
Fit for purpose
And any service must be as described and carried out with reasonable care and skill.
If no price is specified then the price must be “reasonable” and if no timescale is specified the timescale must be “reasonable”
If on the other hand goods are being sold by a private individual to a private individual, they only have to be as described.
In the case of a vehicle it also must be roadworthy otherwise it’s a breach of section 75 of the Road Traffic act.
Under the Consumer Rights Act, all liability is on the Seller not the manufacturer.
Within the first 30 days you can reject goods which are not of satisfactory quality, fit for purpose or as described. However the non-compliance must be substantial.
For example you could not reject a motorcar because a bulb had gone.
On the other hand you could reject a bulb which didn’t work.
After 30 days the retailer is allowed one attempt to repair and if that fails then you have the final right to reject.
Don’t get excited.
Even though you may have the right to reject within 30 days or the right to reject after 30 days after a failed repair attempt, actually being entitled to reject and get a full refund or after 30 days partial refund (less an amount of money for any use which you have had) and getting the money out of the retailer 2 different things altogether.
Car dealers are particularly difficult and I have never yet known a car dealer beatifically roll over and agree to refund even when the engine blew itself to pieces in the new vehicle which was just a week old.
Some reading: https://www.mylawyer.co.uk/buyers-rights-business-to-consumer-sales-a-A76062D77562/
In your case, you would expect a laptop to last longer than nine months and it seems disproportionate that its GBP350 new and GBP300 to repair.
I must admit I have had similar feedback with this company before.
What can you do? Basically take the retailer to the Small Claims Court for whatever the cost of the fix is.
You need to put it in writing that unless they agree to do this by, say, no later than 4 PM on Friday, 24 September 2021, you will issue Small Claims Court proceedings without further notice.
There are unlikely to agree but usually they will settle out of court if you do issue proceedings. I have had it happen like that with computer sales companies in the past and mobile phone suppliers.
Thank you for letting me assist you with your legal question. I am glad that I was able to help.
I am not certain whether that answers the question for you or not, but I am happy to answer any specific points arising from this.
It will be my pleasure to help you again either further with this or any future questions you have