Hi,
The "slot in and twist" guttering clips I have on my conservatory are part of the Wendland Conservatory roof system. These clips hook up into the front inside of the gutter and then you push the gutter up into the rear of the clip until it clicks into place. If you look at the picture of the guttering on the Wendland website you can just make out the design of the clip. When I rang Wendland about the broken clip problems I was having they told me to email Ultraframe Conservatories with your requirement, i.e. number of clips required + postal address, and they will send them to you free of charge. These are specialised clips and as far as im aware they will not fit any other manufacturers guttering.
I received my clips within a few days, enough to do all the guttering. The advice they gave me was to use one clip every 1/2 metre (minimum).