Oh dear, they do look bad - corky areas develop from damage, whether that damage has been physical or from an infection or from insect infestation. Yours have obviously had a problem for some significant length of time - scale's a possibility, information here
https://cactiguide.com/cactipests/#scale
but to be honest, they look so bad it might be too late - any corky areas present from damage will always now be present, even if you cure the problem they've got. Not sure what the whitening is on the Opuntia - looks almost like a fungal growth, but hard to tell from the picture.

How old are you cactus?

The top picture might just be maturity coming on for that species of Euphorbia. It tends to have a tan and gray scaly bark on its older branches.
The same might be true for the Prickly Pear in the lower picture, but it doesn't look normal. If it was here in Arizona, I would suspect scarring from a bad infestation of cactus bugs or Cochineal scale. Slight frost damage, or chemical burns from oil-based sprays, can have a similar effect.

Thanks. The cacti were presents some years ago when they were only about four inches tall! Is it possible to take a healthy cutting from anywhere and start again? I'm not much of a cactus person as you might guess.

Bother I wrote a quite long reply yesterday and it isn't here! Corky scab is sometimes caused by overwatering but not sure thats what this is. . You can't undo the damage once done. Yes you can take cuttings. If there are any unaffected pads on the opuntia (prickly pear) you can cut them off at the join and root them into very sandy gritty compost, kept dry until well rooted. Wear gloves because of the little barbed hairs. If you do get some stuck in your fingers they pull out with elastoplast or sellotape - don't rub them or they will break off.If there is a clean area on the tip of the columnar ones you can simply cut it off and root it similarly, but after cutting it off you should leave it until the cut has dried before planting. If you have any flowers of sulphur it wouldn't hurt to tip the cut part in that.