Rupert - I finally managed to prune my apple tree. I did it on Saturday, a bit later than I had hoped but I was otherwise occupied.
I am not sure I have done the haircut as you had suggested and it was difficult as the tree is very tall and I was using a saw to cut off the branches. I managed to cut off the very big branches and avoided accidental damage to the fence and also apart from a few scratches I came out of this unbruised.
I attach a few photos before and after of my handiwork 
I think I should trim back a bit more but I didn’t want to stress the tree and I forgot to ask permission to trim. I feel bad about that as I am sure the tree will have been shocked when I started hacking away 
I am hoping to pick out a few branches that I can season with a view to making a walking stick or two.
I am sorry - I was not aware that Saturday is not the day for pruning apple trees. Maybe that is what happened last time - we pruned the tree and it went into a sulk and we had to wait a whole year for it to cheer up again, but it did forgive our foolish ways and rewarded us with a bumper crop the following year which was all gobbled up by our resident squirrels which have now sadly disappeared
I think I follow what you are saying, but this terminology of leaders and whips is new to me and so I am trying to digest all this information.
There are trees in the neighbouring houses which may be affecting our apple tree and may support your suggestion of shooting its leaders high.
I was not aware of the crossovers - to me they are all branches but as I understand it, these need to be pruned back. I’ll note this and if I can do it I will.
Summer pruning - again, noted.
Twines - I think you are referring to the washing lines that I have hung up. I am sorry of using the apple tree for tying washing lines is another faux pas on mother nature but that is what the twine are,. They are not trying to guide the tree, though as it is at the fence we have tried to guide it more inwards to our garden and hence there is a slight lean
Thanks for the tips.
Washing line 
Hi Rupert - What advice would you give for this?
There are some “saplings?” at the base of the apple tree and also near the fence an offshoot from the trunk.
Should I keep these or will they affect the main tree?
I am wondering if I should let them grow this year and then maybe cut down the old tree next year, though I am reluctant to do that. I don’t know what the lifespan for apple trees is, but this tree is possibly over forty years old and it actually been replanted - we took it with us when we moved houses.
The haircut doesn’t seem to have stressed it and it will be interesting to see how it turns out.
These are suckers, get rid. The one on the right however can be carefully cut out from the root and it should have some roots attached. Technically, you could pot it and cultivate a new tree from its mother but may not be the same type of apple depending on the rootstock used for the mother tree.
Will they affect the main tree? Aye, they will suck life from it as they compete to grow.