Last November I bought a 2-year bare-root family apple tree from
Blackmoor. On M26 stock I have Discovery, James Grieve and
Sunset.

After planting I cut back the branches by about 1/3.

It is healthy, but has not put on a great deal of new growth, and
I am unsure exactly when and how to prune again.

They have help and advice on their web site
http://www.blackmoor.co.uk/pruning.php

Yes, I have already read that, but am still having difficulty in
applying it to what stands before me. Some of it, taken
literally, would remove more than this year's growth, which can't
be right.

I think they mean pruning of the NEW growth.

If you don't have much new growth, then check it's general conditions.
Is there competition from other nearby trees or near a headge or
fence - what's growing over the fence? Is the soil is poor health or
overlying heavy clay builders rubble etc.

If so sort that out and prune the new growth back a bit harder than you
did last time.