Ok - planning permission NOT required for an extension to a terraced house if:
1)The total cubic volume of the extension (and any previous extensions built since July 1948) would not exceed 50 cubic metres.
2)The extension would not exceed 4m within 2m of the boundary
3)The extension would not be nearer to any road or public footpath than the existing house
4)The property is not listed or within the Norfolk Broads/national parks etc.
5)No part of the extension, including foundations and guttering, would encroach over the boundary.
From what you've said, it sounds like the guttering may encroach over the boundary and so it'd be worth contacting the local planning department to ask whether they'd see this encroachment as warranting enforcement action/the submission of a retrospective planning application.
With regards the window onto the boundary, if planning permission isn't required, then there is nothing you can do about it. If planinng permission is required (even retrospectively) then you could object on the groundds of loss of privacy and the planners would take into account your objection in assessing whether planning permission should be granted.
I'm no expert on building regs but do know that some structures don't require building regs depending on the type of construction, what services (i.e. hot water etc) would be required and so on. But the local building control surveyors should be able to advise.
I think it's pretty rotten when people build without consulting neighbours, at least showing the plans for you to look at. Just plain rude IMO.