Let's start by separating your statutory rights from the guarantee.
Your statutory right to receive a product which is 'fit for purpose' is with the retailer. If something goes wrong with the product it's the retailer who must put it right but ONLY if there is an 'inherent fault'. (i.e. something which was wrong with the product at the time of purchase). For the first 6 months after purchase there's normally an automatic assumption, in law, that any problem which occurs must be due to an inherent fault. Thereafter it's up to the purchaser to show that the problem has arisen due to an inherent fault. (The time limit for such claims is usually 6 years but it can be less or, occasionally, more).
So to claim under your statutory rights you need to be able to show that the problem has come about through, say, the use of poor quality materials at the manufacturing stage (rather than, say, the use of aggressive cleaning chemicals by you). Without finding, and paying, a specialist in order to get an expert report on your flooring, that could prove extremely difficult.
A guarantee is completely separate to your statutory rights. Whoever issues the guarantee (whether that be the manufacturer or the retailer) is free to set their own terms and conditions in relation to that guarantee, and to determine its length. It's normally manufacturers, rather than retailers, who issue guarantees so (assuming that applies in your case) you need to claim against the manufacturer, not against the retailer, if you're relying on that guarantee rather than your statutory rights. As far as a manufacturer's guarantee is concerned, the retailer has no responsibility whatsoever to put things right.
So decide whether you wish to try to claim under your statutory rights (which could prove difficult without an expert's report on the quality of the vinyl) or under the guarantee. If it's under the guarantee you need to contact the manufacturer (or the manufacturer's UK agent, where appropriate).
If (unwisely, in my opinion) you decide to pursue the retailer, I doubt that Trading Standards would want to get involved. They'd tell you that it's a civil matter, and that you should pursue it through the courts. If you decide to do so your first course of action would need to be a formal letter to the retailer, stating the amount of money which you're demanding, and the reason why. The letter must show your own name and address, and that of the retailer. It must also be dated and clearly state that if you don't get your money within a specified period of time (I suggest 21 days) then you will commence legal action. The letter should be sent by recorded delivery, with you retaining the proof of posting and a copy of the letter. Then if you don't get your money you can commence a claim using the online process offered by Her Majesty's Courts Service:
https://www.moneyclaim.gov.uk/web/mcol/welcome
However, without an independent expert report, you could lose the case and end up out of pocket. I still see pursuing the manufacturer, under the term's of the guarantee, as a better option.
Chris