is it a council house you are renting?,
the housing association i work for allow residents to erect there own fence up to 1 metre(out of there own pocket), as long as you write to them asking for permission and detailing why you want it, (kids to be safe,blah blah blah) so i don't see why neighbouring dogs wouldn't come under that section if its a council place,
also would need to be a decent fence not some shabby thing thrown together from all different types of wood we do get them with nails sticking out and so on and they are swiftly removed, also if the properties grounds are maintained by the council and its classed as a communal area that could be an issue
all depends if you want to spend on a fence while renting, if you plan on staying awhile it might be worth it,