Thanks everyone. I'll try to clarify and reply all.
Posted by Les Jones 1 on 26/06/2015 19:50:53:
You also need to confirm that the axis of the tailstock is parallel with the late axis or tilting up or down. Check if the height error is the same with the barrel fully extended as it is with it fully retracted.
Yes, this was confirmed. It is reasonably accurate that I don't want to change it.
Posted by Bowber on 26/06/2015 22:21:26:
If you just shim one side of the head you'll introduce a twist into the bed which will make it almost impossible to turn parallel, as Neil said do any work on the tailstock. Take your time and do lots of measuring as you go.
How high is it?
I don't see why there would be a twist in the bed because of that.
I measured it a while ago and I have to make an adapter to make get a more accurate measurement, but it is approximately 0.3mm too high.
Posted by Frank.N Storm on 26/06/2015 22:47:41:
If you put a shim on the flat part on the bed (I hope I understand the construction of that lathe correctly), you will not only move the spindle axis a bit higher maybe, but you also rotate the headstock around the vee and so the axis moves also towards the operator side. Is it that what you want?
You're right that this would happen, but the side alignment of the tail needs to be adjusted anyway and would need adjustment once I disassemble it to adjust height, so the head moving towards the operator by a small amount is not an issue…
I was worried about this too but two people who have used both methods many times explained that shimming the headstock this way on this lathe is "standard" and would be the most accurate. Obviously the shims would have to be about twice as thick as the height misalignment.
Posted by Frank.N Storm on 26/06/2015 22:47:41:
Up to now no one commented about 'lapping'. How do you plan to do that? With an oilstone maybe? To remove 0.3 mm with lapping you would need days or weeks imho…
My only way is to use a flat surface (granite) and put sand paper on it, sanding the tail on it by hand. Yes it's probably a bit slow… maybe even unrealistic… plus the risk of ruining alignment from the sanding, even if extremely careful…
Posted by Frank.N Storm on 26/06/2015 22:47:41:
I would advise you to find someone with a milling machine and mill away 0.3 mm on the sole of the tailstock, then (if done correctly) you don't have to worry about ending with a tailstock pointing towards the sky…or the other way…
Unfotunately not really a realistic option… unless it's the only option. I don't know anyone, would need to find someone in another city probably, have no idea if they are good and trustworthy (huge issue here) and this kind of thing is not really done here by shipping. there isn't a machining "group" here or anything like this… you almost have to know abotu someone by coincidence. There are a bunch of high level CNC machining places that wouldn't agree to do this or charge a fortune…
Posted by Bandersnatch on 27/06/2015 01:01:29:
Is this a new lathe? if so, I'd send it back (or perhaps just the tailstock).
It's a new lathe and driving to return it (a hassle… no shipping) could result in another lathe (if it's in stock, probably not, as I need this very specific model) that has who knows what other issues. Especially after I spent almost 30 hours adjuting it already… maybe finding someone to mill it is a better option… 
Thanks again