Toolstation's 40 piece Silverline tap and die set, currently priced at £34.84, is described as "made from tungsten steel". I bought a set chiefly because it contains taps and dies of two different pitches for each size, and it struck me the set might be useful for that reason.
I've also got the Aldi set, which was £14 when I bought it a few years ago. I think that one is just carbon steel. The first holes I ever tapped were with the Aldi set – 8 blind M3 holes in mild steel about 10mm deep. Fortunately I tapped all the holes successfully even though the only tap supplied was a taper tap.
I think the taps and dies in both sets are serviceable but I don't think the same can be said for the supplied tap and die wrenches, which seem nearer in consistency to cheese than metal. Fortunately there are plenty of better wrenches to be had for not much second hand.