Extremely poor service Dyson and @home

Purchased a Dyson vacuum from @home in Design Quarter in June 2023 and it broke in January 2024. Dyson and @home are both refusing to pay for the repairs as I have lost the original receipt despite showing them Proof of payment to @home on the day of purchase. Surely they should have the serial numbers of the vacuums they supp**** to @home to track. This has been going on since January and they still have the vacuum with them.