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May be that you'll need to go the complaints route, mentioning the CRA.
Mentioning that you're not raising it as an expired warranty issue, but that you'd reasonably expect the machine to not fail so soon through normal use etc.
This stuff
https://www.moneysavingexpert.com/reclaim/consumer-rights-refunds-exchange/
https://www.moneysavingexpert.com/reclaim/how-to-complain/Did you buy it with a credit card? That might be a route if Dell are unhelpful and you've shown that you've given them an opportunity to do the right thing.
Might be worth looking into the Consumer rights act, as warranties aren't the be all and end all.
You should expect a laptop to last more than 15 months, and as such are covered by the CRA (formerly Sale of Goods act)