It's important to realise that manufacturer warranties, if offered, are effectively an insurance-backed product which act to reimburse dealers for parts and labour costs incurred in delivering the warranty. This is how it works in mature industries and there's no reason why it shouldn't work this way in the bike industry.
However, it is important to note that these warranties always contain a clause that they are "in addition to your statutory rights". Indeed, it is illegal for them to be otherwise.
Statutory rights are conferred by the Sale Of Goods Act (SOGA). If you paid for all or part of the cost of the bike on dealer finance or a credit card (CC), you have additional rights under the Consumer Credit Act (CCA), which makes the credit company jointly responsible. It's worth using credit for this reason alone.
Under SOGA, your contract is with the person or company to whom you hand your money, i.e. the dealer. SOGA states that goods supplied must be "fit for purpose" and "of satisfactory quality". Another point worth noting is that if an item breaks within 6 months of purchase, it will legally be deemed to have been faulty at the point of supply, unless the supplier can prove otherwise (in practice, difficult to impossible). From 6 months out to as long as 6 years, the law takes into account expected lifespan of the item, wear & tear, price paid, etc.
So, if your bike breaks down within 6 months and you haven't caused the breakage by using it outside its expected parameters or by modifying it, then the dealer has to offer redress in the form of repair, replacement or refund, irrespective of any other warranty which may apply. You as the customer have to give this dealer the opportunity do so, and he has to do so within a "reasonable time".
So, if the dealer can't fix the bike, either because he doesn't deal with the brand any more, or parts are unavailable, he can replace, refund, or offer you a loan bike until yours is fixed.
If he won't do any of these, then your best course of action is to send him a letter headed "Letter Before Action" stating the facts and asking him to remedy the situation within a "reasonable time", which you specify (14 days is often legally regarded as "reasonable"). If no response, or unsatisfactory response, then you can claim via Small Claims Court (SCC), which is straightforward (if the circumstances are straightforward) and inexpensive.
Exception is if you bought on credit, in which case you can claim the full amount back from the credit company, even if you only paid part of the cost on credit. This is usually faster than going via SCC. They reclaim from the dealer via chargeback. If the dealer has gone belly-up, then reclaiming in this way may be your only form of redress (the bike of course becomes the property of the finance company).
Sorry about the long post, but it appears that some on this forum have not taken advantage of their statutory rights, probably through not being aware of them.
Phil