If you mean by "VAT registered independent bmw garage" as being a non-authorised BMW Dealer
No.
Block exemption rules do not apply to motorcycles (like they do cars) and BMW will have the right to refuse Warranty Claims. So the law won't support you in upholding warranty claims.
But, the Sales of Goods and Services Act, Section 75 of Consumer Credit Act, Motorcycle Industry Association and Mediation Services might help you, and will uphold your legal rights under other laws designed to protect the consumer, if you were unhappy with your purchase for any reason... and that supports a claim for faulty goods up to 6 years after purchase.
It's not against the law to service your own motorcycle, using Genuine Parts helps your case that standards were upheld and adhered to.
Everything else is down to negotiation, tactful wording and a sensitive approach. Knowing each others position helps