The basic lean-to conservatory has a square or rectangular shape with just a 1-sided sloping roof. The uncomplicated nature of the roof helps a lot to keep the overall cost of lean to conservatories down.
Price Guide 2018
Broadly, there are only a couple of main products that you should consider, primarily natural gas if you have it supplied to your home, and those are:
if it's going to have more than 30 square meters of floor area then you could be looking at needing planning permission to build it and that is going to add something to the Orangery Cost.