You can get to T4 airside fairly easily, there's a bus as shown on the diagram above and usual transit security - they give you a sticker that allows you back into T1 etc and as not many people do it, the transit security isn't too bad. You don't need a BP for the terminal you're visiting.
I've never tried to get into the CX lounge though, the BA one is OK in my experience. In fact I've only even done the T4-T1 route, and that was when flying Air Asia and we wanted to get to the childrens' play area during a 3 hour layover.