Under SoGA they have to make good “within a reasonable time and without causing significant inconvenience’. I’d say not having a washer for three months would constitute a significant inconvenience. Whatever Kenwood tell Curry’s is not your concern, that’s their problem.
On a three month old appliance I’d be chasing a replacement or a refund.
Your contract is with Currys, not Kenwood, so legally you go through them.
Not quite. Legally, they have to make good, but there’s nothing to stop you approaching Kenwood directly instead if you think you might get a better service, it’s just that Curry’s can’t force you to do that as it’s their responsibility. (And if you do approach Kenwood directly, they can decline to deal with you if they choose.)