Malcolm wrote:

We have recently established some autumn-fruiting raspberry canes and
are now picking a small bowlful every day.

Several, though not all, of the plants are currently sending up one to
three new canes - the longest are now 2-3 feet. As I'm going to be
cutting all canes right down in February, I'm wondering whether I
shouldn't cut these new ones down now, so that the plant isn't "wasting"
energy on them. Or won't they make any difference either way?

Yes, probably cutting them would be ok. I always leave a few of these
canes when I do the January (or Feb) cut down - these will fruit in late
June to July. Mine fruit just before my summer fruiting rasps - extends
the season a bit.