Last year our apple tree went a bit crazy and grew hundreds of vertical stems straight up, resulting in a huge amount of leaf cover and relatively few apples.  Now the leaves have mostly fallen off (that was an entire recycling bin filled) you can see what I mean:

So any apple tree experts in?  How would I best prune this to get it under control: it’s far too high and thick with these new vertical shoots, I’d prefer a lower/wider/thinner apple tree.  I’m thinking if I make relatively few cuts through the existing branches where the new shoots have come out from then that might be a job I can manage myself, but would that help or just make it worse next year?  Should I just pay someone to do the right thing?

RHS website has some good advice. When we prune our apple trees we basically try to go for an open goblet/wine glass shape and remove any branches that cross over with each other. Good luck.

Oh great, so the vertical shoots are called watershoots and the RHS site has an entire multi-year section on controlling them.

Just cut mine down. Sad to see it go but the apples were getting a royal pain in the arse. Absolutely **** thousands of them this year!!!

We have about 15 apple trees of various sizes and ages. Last winter I took off about 20% of the branches.

You want to get rid of the new growth, aiming for an open shape. The goblet shape for your tree looks about right. That is, open up the centre of the tree. Reduce the height. Make sure you cut above a node. Remove dead growth. Remove any branches that cross. Make room for the blossom. Fruit grows best on older stems. Leave some new growth that is pointing in the right direction (ie snip branches that are going to grow across others/into the centre/up, leave shoots that will grow out).

This year we had an amazing crop of apples.