Hi
Technically you cannot extend a warranty, A warranty is a statement that is automatically implied when you make a new purchase. It effectively says that the goods are free from defect and are fit for purpose at the point of sale.
Your warranty exists between you and the seller. It has no defined time limit. In some cases you can enforce a warranty claim for up to six years from the point of purchase under the Sale of Goods Act, though the older a claim is the harder it is to verify the claim, and the sellers liability also diminishes with time.
What most manufacturers offer is a guarantee, this is a statement of intent, and it sets out how the manufacture will respond if certain faults arise. It also usually allows you take the problem to any participating dealer. This is always in addition to your statutory legal rights under SoGA. it can never override them.
Extended guarantees are always an insurance policy. They make money for manufacture and the insurer.
In quite a number of respects an extended guarantee is not always required, as you may still have a remedy direct with your seller under SoGA, But SoGA requires the fault was either present at the time of sale or the product has failed to perform reasonably. Sometimes this can be difficult to prove, and this is where a extended guarantee can be easier to use.
Because it is insurance, it can pay to look around to see what else is on offer. A policy with an independent insurer may allow you to have repairs carried out at a wider range of garages, and the premium costs may be better.