Apple Tree pruning experts: should I prune off the lower branch on this Russet Apple Tree?

You are " over thinking" this situation, example : Well if i do this....but, on the other hand. If you are unable to make a decision as far as that lower branch, leave it as it is. If you would like to make a decision why not do a coin toss..head or tails. If no one else gives you experienced advice I hope this helps you.

Certainly looks as though it was intended to be fan trained.
Does the land on the other side of the fence belong to you? if not be aware that the owners are entitled to cut off anything that overhangs it.
If you don't own that land I'd be inclined to encourage the lower branch and also the thinner one above it on the other side, though shorten it to encourage it to thicken up.
Re deciding what to prune, as a general rule you only need to take out all crossing branches and shorten or remove weak and spindly shoots to encourage fruiting spurs.

That's just what I'd do though - you'l probably get some better advice. there are lots of nurseries specialising in fruit trees in Oxfordshire - perhaps there's one near you where someone could be persuaded to have a look and advise you (probabaly at a price, but it might be worth it)

You are right at the tail end of the winter pruning season, so if you want to prune your apple tree I would get a move on before it comes out of dormancy.

Because of its location it's best to train it as an espalier (or similar idea), ie laterals from the trunk trained up along the fence using horizontal wires. I'd forget about fruit this year making the tree shape more of a priority. Cut/saw the trunk back to a point just above the fence. Keep laterals below the fence eg the bottom right hand branch sloping up. Cut back the first lateral off it that leans the wrong way past the trunk back to the branch. Shorten any more laterals along that branch that are crossing back to any spurs.

On the left side there are no branches other than the one big one coming towards the path. I'd cut that back to allow 2 - 3 laterals off it to develop towards the fence. It looks like there are laterals coming off this branch near the trunk.They can be trained in. So cut back to just above those laterals. Give the tree a good feed 2 - 3 handfuls around the base of slow release fertiliser (Rose fertiliser is fine) and hand fork it in.

When the tree comes out of dormancy it should throw shoots vigorously. The ones that come off the trunk that run below and near or along the fence you should retain and train them by tying them in. Cut out most shoots that come out towards the path or shorten them back by half in August, removing all excess shoots or those that cross each other. I'd retain no more than 7 shoots on each side of the main trunk.

Just out of interest Bendipa, how long would you allow the laterals to grow? My first thought was an espalier and then I thought about how near that well trained rose is on the left. Would there be room?

Well the rose looks like a bit of a tangle so that can probably be pruned back as well which would allow more room for the apple laterals. Maybe 2' - 3' would be enough room to let those grow. On the right hand side the laterals could be grown even longer.

Let us know what you decide Jensen? Sounds the best solution all round.

Thanks for you replies, they are very interesting and I will read them again. First of all I need to prune a couple of blackcurrant bushes on the other side of the fence - the first time I have ever done it, but fortunately it sounds much easier than pruning a tree. There is also a redcurrant bush and a gooseberry bush, and as you say regarding the Russett Apple tree Bendipa, I need to get on with it.
The land on the other side of the fence is part of our garden Steragram. First of all are the bushes that I just mentioned along side the fence, and then there is path along side of them, and along side of that is a lawn. The idea is to encourage the tree to grow in this direction, though I have just realised that it might look quite nice overhanging the driveway too.
Yes, that it a rose bush on the left, which has not been pruned recently at all.
I am really interested to hear that the apple tree can be trained as an espalier. But how long would it take to yield apples again if it was pruned so hard? The other snag is that the fence has been there since we arrived, and it does not feel sturdy. I have noticed that that post moves easily if I press it. Perhaps water has got into the bottom of them over time, and started to rot the wood.