Panic is correct - this is the usual arrangement.
Whilst the neighbour does legally own the land of the driveway, you normally have right of access to pass/repass, any maintenance costs are shared, and there will be a specific convenant to prevent him from parking on that driveway.
You don't normally need a solicitor to sort this out - money for old rope, Get on the Land Registry website, type in the postcode, select the property, pay the �3 x2 to download the Land Register and the Title Plan and read it.
http://www.landreg.gov.uk/
Very unlikely your land is not registered with LR.
This is only true of the driveway itself - he can maintain the rest of the open area which he legally owns as he pleases and it is up to you to paint your part of the fence (if you wish to).