http://www.screwfix.com/p/erbauer-erb620htl-250w-multi-cutter-220-240v/2570g
Something like this would do the job I'm sure. I have one and providing you let the tool do the job and don't force the issue it can cut very accurately in confined spaces.
There is a tendency for the blade to 'drift' a bit but the way to deal with that is to mark exactly where you want the cut and again, let the tool work at it's own speed.
Edit: Mrs Colly was just nosing and asked:'How would the blade get to the back of the pipe?'
Not a daft question but the solution is to cut out a section of the pipe to enable the tool to get to the far side. You're going to lose 400mm plus so there's plenty of room.