I think the little branched one is an opuntia of some sort. Be careful handling it as the little white hairs are barbed and will stick in your fingers. If that ever happens put sellotape or elastoplast over the place and they will peel off. Don't rub them of they will break off leaving the barbed end in your skin.

The one that's flowering I'm pretty sure is a mammilaria. It may set seed which you can grow on if you want to.

Hywel will be able to tell you a lot more than I can.

Thank you

I suggest looking at Hywels blogs and photos too.....his are a delight

1st photo = Opuntia vestitia

2nd photo :-
the big one = Pilocereus azureus
the one in the back = Mammillaria spinosissima
the other one - not sure ... could be a type of Echinocereus ?

They look as if they need repotting.
Also give them a feed, and keep them in a sunny place.
Water them well in the summer.
Keep dry and cool in winter.

The Opuntia and Pilocereus will not flower in the house.
Mammillaria will flower easily every spring if given the above conditions.
The Echinocereus (if that's what it is) may also flower if given the above conditions.

Good luck ! :o)

I've looked again. I think the one I named Echinocereus is probable a type of Pilocereus. It won't flower in the house.

Thank you very helpful can I ask how I re pot them as if never done it, and is it ok to keep them all together?

Use cactus compost which is more open and gritty than the usual sort. Wait until your current compost is dry. Tip the pot to get loose grit put of the way. Either wear thorn proof gloves or wrap each plant in several layers of newspaper to protect your hands and tip out carefully onto the bench. Do not touch the opuntia with your bare skin.

You can pot them in a larger pot (with drainage hole)all together but repotting another time is a lot easier from single pots - the choice is yours.
Examine the roots and the inside of the pot for white fluffy stuff. Root mealy bug tends to appear when plants have been pot bound for a while. If you see any paint it with meths, using a child's paint brush. If you choose to pot them all together you will have to find some ingenious way of supporting them while you get them into position -again rolled newspaper is useful. Ease the new compost around them. It will be dry and easy to pour in. When you are satisfied that they are secure and arranged as you want you can and plants them off with coarse grit. Don't do as you would for other plants - they won't appreciate a good soaking immediatelyafter repotting! This is what I would do - perhaps Hywel will have some other suggestions.

I think you've said it all Steragram :)

Thank you so much for all your help i will be re potting this weekend just need to get some cactus compost.