I have two bench grinders just a couple of years old, one is a Wickes own brand and the other came from ALDI I think, but both were made in China and both have the same problem. Take a quick look at the "shoulder" on the shaft here:
**LINK**
The 50mm dia. wheel flange slides onto the 1/2" dia. shaft and locates on that so-called shoulder. As you will know, the grinding wheel is then fitted and secured up against the this flange. But without an adequate shoulder my newly fitted thinner wheel now has a sideways wobble so bad that it's not safe to run the machine up to top speed. The only way the Chinese got away with it is that both machines originally came fitted with wider grinding wheels with 1/2" bores that were a good fit on the shaft. Lateral stability here relied more on the good fit in the bore and the shoulder was demoted to a "stop".
Both the shafts on the two grinders look so similar that I would not be surprised if they came out of the same factory. Because of this I am reluctant to buy a replacement machine in case I end up with the same gash ole' rubbish. I know I could pay more and get better, but for me, half the fun is doing it on the cheap.
So I have made a simple replacement for the inner flange. I machined the bore so it is a snug/tightish fit on the shaft and because the new wheel is quite thinner than the original I could afford to make the new flange nearly twice as thick as the original.
**LINK**
So once again the tiny "shoulder" is no longer a register but a "stop" – a la chink. It's not a perfect solution but the wobble has been reduced to a very usable light quiver.
Dressed the new coarse white wheel (much better for HSS I think) with one of these great bits of kit:
**LINK**
Wish I'd had one when I was doing my T&C grinding stint back in the 'eighties. It's much better then a single point diamond .
Anyway, reading around the forums I was under the impression that Chinese engineering had improved no end over the last few years but these grinders and my woefully inaccurate Chinese drill press make me think otherwise. I'm glad I've got a French lathe. 
ATB
Stuart