Hi Moonlight,
The fact is that construction has come a long way since the days of leaking flat roofs that absorb solar radiation and lose their integrity after a few years.
Modern flat roofs are ventilated and insulated to protect effectively against the elements- the greenhouse effect you mentioned- and maximise clear head room across the floor area of your extension. You can incorporate rooflights into a flat roof to increase the ingress of natural light and really open up your new space. Roofing membranes are now quite advanced and a good roofing contractor will give you a 15 year guarantee against leaks with the high performance products lasting for around 30 years (although the manufacturers will tell you they last for longer than this).
Depending on the layout of your property, a pitched roof can be a very effective way of constructing a side return extension and depending on which borough you are in, this can be the approach that the local authority planning department are more likely to look favourable upon. A fully glazed pitched roof can be manufactured and installed by specialists which can be very effective. While you will get solar gain in the summer and some heat loss in the winter, this would be offset by incorporating higher performance insulation in the walls and floor.
We're an architecture practice based in Wandsworth if you have any further questions or require any further assistance please don't hesitate to get in touch.
www.draw-architecture.co.uk
Kind Regards
Jamie