To answer the OP's question. Yes. I think you should have a look at repairing your DMM. Those old Precision Gold meters (Maplins, I presume?) were pretty good.
Chances are it's just dirt on the switch contacts. Take the meter apart and clean them with a cotton bud and some IPA.
If it's not the contacts, it could be a dry joint. Check the meter over in bright sunlight.
In this day and age, where everyone throws everything away and repairs nothing, and people upgrade every other week to the latest iphone, I think people should be positively encouraged to repair things.
And I agree 110% with VK6ZGO, above. VK6ZGO struck a chord and made me post to a thread I've read but wasn't going to post to.
Everyone gets far too excited about CAT ratings and true RMS.
When I first started (work I mean, not hobby tinkering) 30 years ago, meters were naff-all rated. And true RMS meters were made by Fluke and Bill and Dave, lived in the lab and cost five grand, and some.
And there are true RMS meters and true RMS meters. My Fluke 87IV can measure the AC and DC components of a non-sinusoidal waveform.
Many true RMS meters (such as the Fluke 179, and probably the Fluke 87V, although I haven't checked; before all you 87V fanboys jump down my throat) can only measure the AC component.
For, as it were, true, true RMS measurements, you need a meter with a thermal converter, such as a Fluke 8920, or an 8520.
And, as VK6ZGO says, if your waveform is that distorted; you're probably better off with a scope.