Everyone seems to have a favourite time and way of handling this. But in
general, cut back, under the dead flower heads, to the first strong,
healthy leaf buds each year in March if the danger of heavy frost has
passed. Take out any thin, weedy and crossing stems. Some people say
that if you prune all of the stems back you're likely to end up with no
flowers, so they cut back one third each year. I can't say I've ever
noticed that as a problem, so it's possible that depends to some extent
on climate and when your plants get going each year! OTOH, if you're
renovating old plants that have got weedy and out of control, risk
sacrificing the next flowering and cut them hard back to the base leaf
buds to encourage new, strong growth. Quite a few people leave the dead
heads on them to protect them from winter frosts, snipping these off
when they do the spring prune and tidy up. You could also give them some
bonemeal round the roots and fork it in lightly, taking care not to
damage the roots.

Many thanks for the detailed explanation.

The one that was in full bloom last year has no new shoots as yet, and
no signs of life under the old heads. The one that was mostly foliage
last year now has new shoots all the way down the stems. As one was a
cutting from the other, I thought they would behave in the same way.
From what you say, I had better wait until March and review the
situation then.