Your plant looks like a Pachypodium, which is actually not a cactus. I think it may be getting too much water and I suspect the soil and the pot are holding too much water to allow the soil to dry out enough before watering again. Does the pot have a drainage hole?

If it were my plant I would carefully unpot the plant and inspect it for rot. The dark coloration at the top could indicate rot, hard to tell from pictures but combined with the shriveling trunk I would look at the roots and see if they are dark, mushy or gone.

Can you get some perlite? I would mix perlite with the soil so it's more like 60% perlite (or more) / 40% soil. It needs to be less moisture retentive & dense and the perlite will help with that.

The plant needs a lot of sun (acclimate slowly) and has distinct dormant periods that you have to be aware of as the don't like to be watered at that time much if at all.

Hope this helps, good luck!

I agree with elucas. It's a young Pachypodium, probably P. lamerei. I also agree about the care needed :-) It will go dormant in the winter, although (in my experience) lamerei isn't apt to lose all its leaves in the winter like some of the other Pachypodiums do.

Oh, and I think watering every few days is way too much for a Pachy, especially in the potting mix it's in, and in a glazed pot. I would get it out of the pot, clean the mix off the roots, and pot it into a pot with a drainage hole with a potting mix that drains quickly (like elucas suggested). I wouldn't worry too much about some dropping leaves; that could simply be in reaction to a change in its growing environment.

Oh wow, thanks guys! The pot does have a drainage hole at the bottom, with mesh to stop soil leaking through. but I have other pots and will change the potting mix. Massive help just to know what it is, I've been googling desperately for a fortnight. But this has been a big help, hopefully I can sort out the care so I don't lose it, I'll get some perlite in ASAP.
Thanks again!

Remember how small it is now because if everything grows right you will have a tree. Not a huge tree like a Redwood, but they can get up to around 20 feet. You don't have to worry about that for a long time tho:). I have one and I love it. There so pretty:).

This isn't the first time that I've bought something that actually ends up like a tree....thanks so much for letting me know! How big is yours now?

Maybe two feet:). I planted mine last summer in the ground. This winter it lost all it's leaves, but they're growing back thankfully.

This pic is from last summer. Looking at this pic I definitely think mine has grown.

Recent pic with no leaves. Looks funny;).

Leaves are growing out the top:).

Oh wow, it looks amazing! Won't be able to plant mine outside I don't think (UK weather will kill it) but hopefully I can get a couple feet as an inside plant :)

When it gets bigger you could totally keep in a big pot on wheels and bring it in during the cooler months. I would definitely get some perlite or grit to mix in your soil:).