Speaking entirely as a clueless monkey but with direct experience of which you speak:
Try jump starting it with a mains powered starter thing (whilst its still plugged in). Some cars can turn over great, spark etc.. but not start - battery hasn't got the 'right' oomph.
Does it start if you push start it? Does your battery cell(s) gas when you attempt a start? Perhaps your sparks are wrong (gap too big) or the spark is weak cos your discap is worn out/coked up.

I went to Carland in West Thurrock a couple of years ago when I was looking around for another car.

I've never come across another dealership like it! From the moment that you enter their door you are pestered by one of their "advisers" who really won't leave you alone. They ask you all sorts of questions like what car you're looking for, how much you want to spend and, of course, about finance arrangements. I only went in to have a quick look round, like I had at many other used car dealerships in the area, without all this hassle. They just wouldn't leave you alone.

I was just about to turn tail and walk out when the "adviser" finally agreed to let me do what I had come in in the first place to do; just have a quick look around at their cars for sale.

I needn't have bothered! They were all high mileage examples, hence what seem at first to be low prices, but, when you take the mileage into account, they aren't. Condition of some wasn't wonderful, either, with stone chips on the front being quite common, as were imperfect interiors.

My advice, all things considered, is to stay away from Carland!!!

I am not familiar with the exact details of this design but the 320d is fitted with a dual mass flywheel. Sometimes with these devices, they can go into a resonance if the engine is not cranked for long enough, with symptoms as described. The answer is to ensure that you keep the starter on for long enough. You should be able to note that the starter will autiomatically stop cranking even though the key is still in the crank position when engine idle speed is established.
Peter F

Ah, mechanical fuel lift pump here, sorry...
No trouble with the skoda disappearing yet, just removed the fuse from the "engine control" position, seems to do the trick.
Maybe I should wire a hidden switch in sometime though, in case this happens again?

There's a place called Lepsons in Gillingham 01634 580582. They're a bit out of SW London but did an excellent job on a wheel for me recently which I thought was a write off. £25 + VAT so quite reasonable. They may be a national franchise so give them a call to see if they have a local depot to you. Also check under "Wheels" in the Yellow pages.