What is your neighbour trying to create? Beech can be used to form a hedge. To do this it is trimmed each year & generally kept to about 2metres high. If this is what he wants to do, then I don't think you have any need to worry about the hedge - except that you will have to do the trimming on your side if the neighbour doesn't do it.
On the other hand, if he wants to let the trees grow into mature beeches he is an idiot! These can be massive trees & totally unsuited to a normal garden boundary situation. However, you can't make him take them away but if they become a problem due to height etc. you can involve the Council who can take action under some fairly recent legislation to make him reduce the height.
As has already been said, you can cut off any branches overhanging your boundary (which is, of course, still the line of stakes), but you should tell him in advance you will do this if he doesn't get them cut himself & offer the cuttings to him. You will have to pay for the work if he doesn't do it. But be careful - the appearance of the trees can be ruined by cutting one side off in this way, & it will be your side which will be unsightly.