Hello everyone and thank you for your responses!
Hopefully I'll answer all of your questions.
The controller is an Ipco Studio 3000, it only lets you input a target temp and not a target cone.
Unfortunately, my kiln doesn't have a peep hole, so I'm not able to watch until the cones bend.
The kiln can fire to 1260C and it has one thermocouple.
I wasn't able to get a multimeter from my local store yesterday, so I've ordered one online instead. I thought I'd do a bisque firing while I wait for that to arrive, as I had lots of pots ready to go. And I recorded the temperatures again. Weirdly, the controller shows that the temperatures rises at 100C/hr no problem, until it gets to about 800C and then it starts to slow down again, by 35C/hr, and then 50C/hr for the last 100C. Which confuses me, as when doing the glaze firing it was able to get to 1170C before slowing down. I didn't have any cones for this temp, but the pots came out fine, nice and pink.
When we got the kiln, we noticed one of the wires connected to the thermocouple had snapped off, so we removed the bit stuck in the hole and wired it back in again. Perhaps it has something to do with this? (Sorry, should probably have mentioned this earlier!) I'll get my partner to check again later for any loose wires, and report back.
What I don't understand though, when the kiln is cooling down, I wait for the controller to get below 50C before I start taking stuff out, if the temperature reading was incorrect, wouldn't everything inside be way too hot to touch?
Thanks for your help everyone.