Providing the existing pipework is sound and in good condition I'd personally make a connection onto the existing pipe, outside the chamber. That chamber looks to have been well built, with neat benching, all you're doing by disturbing it is making work for yourself. The existing pipes are salt glazed stoneware, either a 'Fernco' type connector, or I usually use these, from Wickes. http://www.wickes.co.uk/Wickes-110mm-PVCu-Soil-To-Clay-Drain-Connector/p/432046.
Carefully cut through the clay pipe, to give a clean edge, then chamfer the outside edge, then apply a suitable lubricant to the collar and end of pipe before fitting. Carry on from there in 110mm plastic to the house.
Carefully cut through the clay pipe, to give a clean edge, then chamfer the outside edge, then apply a suitable lubricant to the collar and end of pipe before fitting. Carry on from there in 110mm plastic to the house.