Cactus identification

Posting this on behalf of someone who doesn't have a computer...... Would anybody be able to help identify this cactus? Also they would like to know if it can be pruned without killing it off as it has outgrown its current surroundings. It used to be in a hallway but since it was moved to a conservatory it has shot up in size.

Thanks for any help!

 

90% ... Cylindropuntia subulata

very common in the mediterranian area , it could may be an american form ....the flower will tell you

 

yes it can be pruned but not now , wait for summer .... what ever you cut can used to make new plants

 

Yup, Sal, asgree with your id.
From South America, but has been naturalised all over the world.

They grow into small trees.
Personally I wouldn't prune it. But if there is the odd branch getting in the way, no harm in cutting it off.
In fact, you can dry out the cutting, pot it up, and start a new plant.

 

Thanks for the help and identification! The reason i have been asked to find out if it can be pruned is that it has grown to 8ft tall and is now too big for the conservatory.