I have put 3 photos on flickr which show the problem:-
http://www.flickr.com/photos/1362986...7634118941737/

1. The dishwasher waste enters from the left at the lower T but
appears to have no trap(?)

2. There is a leaking split at the upper swept T which is solvent
welded. Probably caused by 3.

3. The washing machine waste has its own U-bend but is unsupported.

I could replace the sink trap with one with appliance hose connector
but would need then to somehow blank off the unused T (dunno how).

Looks like I would have to cut main waste pipe below the lower T and
start again...

Any other ideas gratefully acepted...