Hi,
When you buy something new, it legally has to be "of satisfactory quality", "fit for purpose", and "as described" - see Consumer Direct's website
here. Satisfactory quality includes being suitably durable, i.e. it has to last reasonably well. Any manufacturer's and/or retailer's warranty is always
in addition to your statutory (legal) rights anyway. So even if those warranties have expired, you
still have your legal rights. So, the law might say for example that to be reasonably "durable" any camcorder should last say 3 years, meaning that if it went wrong after 18 months, the retailer might still be liable to give you say a 50% refund or 50% towards repairs. To check exactly what your rights/expectations should be you'd need to speak to Trading Standards or Consumer Direct though. (That also explains why Extended Warranties are never worth buying.)
But beyond that, if it's a recurring problem that first appeared within the 1-year warranty, and Dixons didn't manage to repair it properly (even if it lasted for their paltry 3 months!), then I'm pretty certain they really do have a duty still to sort it out. Again check with Trading Standards to be sure of the details.
Also, your contract is with the retailer (Dixons), and not the manufacturer (Sony), so it is Dixons who are responsible, Sony don't actually have to do anything. I just mentioned it as a last resort, as you might find it easier to get some joy out of Sony than you would Dixons!
I bought my Sony Digital 8 camcorder in July 2002, and by the end of the year, the internal battery and power supply were starting to fail intermittently. By Easter '03 I decided it was a fault so took it back to the retailers, who couldn't find anything wrong with it. Over the next few months, I kept trying it and took it back again 3 or 4 more times, until they eventually found the problem. They then sent it back to Sony, who said it was such a weird fault they couldn't repair it! So in December '03, the retailer gave me a new replacement camcorder - hooray for Hughes! Even though it was then 18 months since I'd bought it, the fault was first reported within the 1-year warranty but hadn't been resolved, so they still had to fix it. Even if the problem hadn't appeared until the 1st year was up, the retailer would still have had a duty (albeit possibly a reduced liability) to sort it out.
Hope that helps, good luck!