The solicitor and the neighbour cannot stop you going ahead with the development. What they can do is stop you getting easements for services or access across the drive. However please read my later comments about just going ahead regardless.
Why did you not get the easement agreed in principle and in writing before you made the planning application? Under the Law of Property Act 1925 and the Law of Property Act (Miscellaneous Provisions) 1989, unless you are claiming an easement by prescription or otherwise through use of longer than 20 years, then any easement must be evidenced in writing and signed by the parties.
If that is not the case, created a problem and the neighbour can now hold his hand out and hold you to ransom. It seems likely he was aware of that and was seeing this as a cash cow and hence, he agreed verbally that you could do this, assisted you in getting permission and now is either refusing or will eventually be asking for a large chunk of money.
If he does want money, there is no formula, it really is as much as he can get away with asking and as much as you can afford without you walking away and telling him to get lost.
If you have used the access which you are proposing to use and have done so for more than 20 years, then there are ways of getting bits formalised but I get the impression that this is not the case. There is no such thing as an easement of necessity unless both pieces of land used to be in common ownership and the easement is a necessity of the land being divided.
At this stage in time, there is nothing you can do to force the neighbour to give you the easement and the more you ask him or argue, the more important he will think this is and the more likely he is to hold out for even more money.
So, going back to the very first point I made about the solicitor not being able to stop you doing the development, I would advise you against doing that quite simply because he will know them that he has you over a barrel.
I’m sorry that the answer is not more favourable for you but what you did do, is get it in writing before going any further.
Can I clarify anything for you?
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