On this one, I really feel that you are going to have to seek professional advice.
If you read the responsibilities of property owners here
http://www.environmen...org.uk/rte.asp?id=103
you will see that one landowner can't claim the water run-off from another landowner's land is his problem. But that's for free drainage. The whole situation changes if some cretin tarmacs over a big area, preventing water seepage through and it then runs off elsewhere to the inconvenience of another landowner.
From what you say, that's what has happened here.
The trouble is, it was a previous owner that did this - it really should have been picked up then - not now. I guess you didn't knwo what damage it would create.
If you are offering to pay for this work, that might be most of any potential argument about money settled overcome, but there needs to be some scope of work agreed in case you cause damage inadvertantly.
Google 'Party Wall Act' - it doesn't strictly apply here (not a party wall) but the sort of legal framework process for resolution could be similar.