You do not need to be to fussy about the thread you use, as long as all the threads are roughly of an even thickness and the same fabric, usually wool, throughout one tapestry.
I have inherited lots of tapestry wool, all different makes and thicknesses, some stranded and also bought job lots at auctions. I mix all makes and brands together. Stranded wools can be separated and regouped into twos, three or fours.
No one looking at a a piece could tell that I had used different brands of wool to make it.
John Lewis? That is if they still stock it. They did a year ago. Lots of places online have Anchor or DMC. Cheaper ones may not be as good quality. The numbers are in groups and are helpful if you want several shades that go from light to dark. DMC colour chart Anchor colour chart You can also do it in stranded cotton, but it is not as thick as the tapestry wool, so you need more than the standard six strands of it. A bit of a fiddle to get nine strands, but it looks very nice and silky when done.
I've had a practice run at this, and I like it. I've practised with ordinary cheap knitting wool but now I want to buy those little small bundles of wool, but good quality. I've looked on line and my heads spinning with all of it. Help needed from anyone who embroiders with wool, where do you buy it.