I would disagree with Androcles. I cant see the landlord getting involved as he cannot control what a neighbour is doing. It would be the same if the neighbour was making a lot of noise, the landlord wouldn't get involved. If it was you making the noise or being complained at for blocking the drive then he would possibly get involved.
Personally, I would be making a nuisance of myself by asking for access to my garage every day, or several times a day, until they get the message. Some people may be under the misapprehension that they have more legal rights than you because they own their property and you rent, but this isnt the case.