Overseeding

Okay, so I've cut my grass short, scarified, aerated and raked in a good amount of compost/sharp sand then I've overseeded the area...

That was three weeks ago this coming weekend and the existing grass that was cut short is in need of a cut, but the new grass is either still young or not yet germinated.

What to do?

 

I would water it, water it , water it and leave it to grow.
The old grass in need of a cut to look good will get on fine
but the new grass will get a chance to grow.
I think you have to give the new grass a chance, then once established you can cut the lot.
It might take two or three cuttings after that to get it to look good but you should have a good, healthy lawn established.

 

To be honest if the seeds have been down 3 weeks and not germinated (providing you've kept the soil from drying out) I'd be worrying. I've just done a major job on my lawns and 3 of the 4 have an pleasing covering of new grass, one is very patchy though and like you the old grass needs a cutting. It took only about 5 days for the seed to germinate on the other lawns so the one that hasn't been a success is going to be cut, re-worked and fresh seed sown.