We have recently completed an extension in which we built right up to (but not over) the boundary, replacing the previous boundary wall with a new one. We had to have agreement BEFORE we started any work. The provisions of the Party Wall Act are very clear about that.
Why, then, are you being pressured into agreeing without any of the time limits and other provisions of the Act being observed? Is it so you won't really have a chance to examine what is being proposed?
It is really important to know EXACTLY what the building work involves, including agreeing access to your land if any. Where will the building go?. Where are the pipes etc? In our case,there was a real problem with a partly buried gas pipe which the (joint) party wall surveyor was very useful in sorting out. You can't leave decisions like that to the neighbour to sort out alone, because the most convenient solution for them could be disastrous for you.
Everything, including access times, moving garden plants and replacing them etc, should be agreed in writing beforehand.
I don't think there is any benefit to you in allowing any building that encroaches on your land-it sounds as though they are trying to cadge a bit of your property without paying for it. The plans and so on should never have been drawn up on that basis without having given you a proper chance to look at them and agree, and without offering compensation.
I would be very cautious. If you are being rather fobbed off even at this stage, you can't have any confidence that the project will be properly handled. What if, in the end, they take up far more of your property than 6", for example?
My advice: ask your neighbours for a copy of the plans and a letter from their surveyor/builder/whatever setting out what they want to do and why. Since they're so keen, they should be able to get you that in the next couple of days. Also, get on to the council urgently and make sure the planning or building control officer comes to your house to view the plans in your garden so s/he can properly assess what is being proposed. It might not need planning permission (because it is a 'permitted development') but don't take the neighbours' word for that. You will also need a party wall surveyor urgently (I wouldn't use theirs, since they seem to be being a bit cavalier)and once you have one all correspondence is better done surveyor to surveyor.
There is no reason you shouldn't ultimately be able to agree something with them, but your house is your major asset, so don't be browbeaten into doing something against your interests.