Looks like one of the echinopsis family of cacti. They like fierce drainage so I suspect you need to re-pot in rather less compost and make sure it is gritty and not multi-purpose.
I'm not much of a cactus person but I can tell you bought it from Morrison's for £5 I can also tell you that the Morrison's soil is ok but not great and they have a habit of planting the cacti too deep and watering them at the wrong time of year. I saw quite a few rotting in the shops. I took mine out of the pot after buying them, removed the loose soil from around the crown of the plant and as much of the other stuff as possible then repotted in gritty soil with a top dress of grit. I still haven't watered mine since buying them months ago and probably won't until late march. The growth on yours could be due to too much water during the winter but as I said I'm no expert.
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I expect @wild edges can help you more.
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