So you're capping a shared supply branch? Will it be live?

You can do it live, but it's much easier if you can isolate the shared incoming main. If you make the branch at your tee as short as possible to cap it, it will comply. The branch is to be disconnected at it's source. As far as I'm aware, there's no regulation stating you need to remove the tee altogether, although if you can achieve this by using one coupler, then it's another option. I find philmac universal repair couplers are the best for this, sold by pipestock.com
Be extremely careful when exposing the shared main, if you damage, flatten or score the lead, you could find your fittings won't seal.
Underground fittings should be buried in the trench, not in a duct, and will be designed for this purpose (plasson, philmac etc or DZR metallic).
4" soil pipe is suitable for ducting entering the property, I usually use it. Insulate the pipe inside it, and fit soil pipe reducers down to about 20mm bigger than your mdpe size. Seal each end of the duct with decorator's caulk type sealant (silicone isn't suitable for mdpe).
There's additional guidance here:-
http://www.unitedutilities.com/documents/1344_How_20to_20lay_20new_20pipe.pdf