Dux,
What plants are in your present hedge, and has it always been 11 ft high while you've lived there?
Flobear's idea is a good one
The best way to find out what you're allowed to do in terms of boundaries is to go and ask the Planning Department rather than guess or take the advice of the possibly badly-informed guesses of others. Planners are very helpful, know the law and often have good alternative suggestions to make.
Don't forget that whatever you do it's got to have appeal for a future buyer of your house or your neighbours', so don't make a problem for them or yourself.
Joe