It depends upon the situation. If you have overgrowth encroaching on your property you can cut it back to the boundary line provided you do not damage (ie kill or weaken) the plants and return the offcuts to the owner. If the overgrowth is blocking light or view you may be able to claim ancient lights, a right to light of older properties. This may requir a legal opinion.
If its just an eyesore it is far more difficult. It is dependent on local bylaws, but the owner of the garden is allowed to do with it pretty much what he likes. So if he likes it overgrown, he may be in the right. There are ways of dealing with eyesores though. try contacting the eho at your local council.
In addition to what Incitatus says, if your neighbour really is preventing you enjoying your garden, he is committing the "tort of nuisance" for which you should be able to get "injunctive relief" i.e. an injunction to do, or stop doing, something. You need to go to court for an injunction, and whether you get it depends on whether it really is a "nuisance" (in the technical, not colloquial, sense).