[MovedGoalPosts]

Make it very clear to Virgin Media that, especially since their field manager has agreed the cable is on your land, all expenses that you incur in proving your claim and their trespass will be claimed from them. Do that in writing now, by recorded delivery, in the hope that they will see sense. You don't need a lawyer to write that sort of letter.

Yes title deeds can be a problem. The plans attached are at such a small scale that they simply show your land adjoins the neighbours, not exactly where boundaries lie. Sometimes there are more detailed plans from when the estate was laid out, but even then boundary markers can move. Unfortunately, if your neighbour is effectively claiming part of your garden as theirs, which seems to be an implication if they are saying the cable should stay there, you may be drawn into a long dispute where there may be no winner over cost. It can get worse as when you try and sell a property a common question is whether you are in or have had a neighbour dispute, and you have to truthfully answer which can put off purchasers devaluing property.