Why isn't my new shower draining properly?

I had a fancy new shower, including brand-new plastic drainage, installed as part of a full central heating/shower installation in December 2008. Within a few weeks, it started to drain slowly and now fills up very quickly. I've tried putiing some very nasty chemicals down the pipe, inlcuding one described as 'industrial' on the label. It made almost no difference.
My plumber is stumped. He is sure the pipe has sufficient slope to take waste away quickly and for the first few weeks this was happening. I could have a full-power, leisurely shower without filling up the glass box like some Harry Houdini stunt. The waste water runs to a pipe on the outside of the building, which doesn't appear to be blocked.

If I want to investigate properly, I'll have to take out the ceramic shower tray and glass enclosure, which I really don't want to do.

Help needed!