Should I cut these branches off apple tree?

[PureBlackVoid]

Bit clueless with trees and I’m don’t know what this variety is, I just know it grows big tough apples.

Branches grow out sideways all over it, the lower ones I cut back (not sure if I should..!), the top is looking a bit messy. Should I leave it be?

If you have iPlayer access, Monty covered pruning apple trees in last week's Gardener's World - worth looking up, maybe?

I don't think you'll harm it (by pruning now) if the branches are relatively small ones.
Ideally prune in late autumn or winter to avoid tree wasting growth effort.
Also avoid summer pruning when disease ingress is highest risk.

Summer pruning is OK if you're not taking off big branches, and doesn't stimulate new growth in the way that winter pruning does, so is useful if your tree is as large as you want it. According to the RHS, summer pruning is what you should use on restricted growth forms such as espalier or cordon.

Summer in this context is August.

I take out branches that go in towards the middle of the tree and ones that cross over. If you want to shorten take back to a branch that goes in the direction you'd like.