Thank you all for your replies.
Unfortunately I don't have any pictures of the trees, but they are quite lacking in branches!
I did do some pruning of the branches - especially the ones that appeared dead and lifeless, but I'm not hopeful of them becoming a bumper harvest any time within the next few years.
The apple tree is only able to fruit around 6 apples, and the plum tree is wrapped at the top of the canopy in weeds, so, I am almost debating whether to just remove them both and plant new trees elsewhere on the plot.