As a rule of thumb I’ve always worked to budgeting about half the price of the coffee machine on a grinder (more here if you want)
The Gaggia is a half decent machine, you’ll need a decent grinder to get the best from it. I’d suggest the Baratza Encore which is about £140 new, you may be able to get it for less second hand.
My parents have the same machine as you, they messed around for ages with rubbish grinders that didn’t get the best out of their machine (including the Dualit one you have), they now have the Encore and are happy with it.
This isn’t coffee snobbery speaking, I just think you will genuinely you’ll struggle to find anything for cheaper that will go fine enough for the Classic.