Hello Wildenb,
Trading standards have given you the correct information. But I think you have not understood the implications of the differences between a manufacturer's warranty and your statutory rights enshrined in the CRA.
These two processes may seem similar on the face of it but they are legally entirely separate, and crucially the law says a manufacturer's warranty cannot (must not) affect your statutory rights. Sadly the buying public are all too often kept in the dark about their rights, as this tends to suit the seller. Under the CRA it is the seller that is always responsible for the goods they sell, and they are liable if the goods are faulty or fail unreasonably.
What most dealers fail to do when a customer reports faulty goods, is to ask if you want the remedy to be done under the Manufacturer's warranty or the CRA, becasue if its the CRA, the dealers profit margin is in jeopardy where as if the work is done under the manufacturers warranty the cost of parts and the majority of the labour costs are covered by the manufacturer. so the dealer will naturally prefer to push you down the manufacturers warranty route.
You may think this is only fair, but the seller has failed a legal duty by selling faulty goods. If they want to avoid after sales costs they should ensure the goods the sell are defect free in the first place.
Critically when you reported the faults to the seller did you specify how you wanted them to be handled? If you just said they're warranty faults the dealer may have assumed you meant having them sorted under the manufacturer's warranty. The consequence of this is that the seller has to wait for authority to carry out repairs under the terms of the manufacturer's warranty terms and conditions. The down side to this from your point of view is the work is now scheduled by the manufacturer and their time scale.
If you make it clear you hold the seller responsible under the CRA, then manufacturers opinion holds no sway, and the dealer is required to proceed with repairs as soon as is reasonably possible to inconvenience the customer as little as possible. This include the cost of transporting the faulty items to and from the place of repair.
The CRA does not seek to give an unfair advantage to either party, but the product you have purchased has failed either because of poor design, materials or manufacture, and that is breach of the CRA. The seller has therefore failed in their duty, and must expect to be held accountable for their failing. How the seller reclaims the costs from the manufacture if of no concern to you and it should not prevent or affect the remedy.