The controller I have used for my home built HT ovens is either the Automation Direct Solo 4848VR or the Omega CN7823. Same controller, different badges. I buy whichever works out cheapest at the time. It has ramp and soak capability and a DC pulse output to drive an SSR (40 mA, so enough to drive 2 SSRs on the strange system you use for 240V over there). SSRs allow shorter output cycle times than relays and this helps with stability. I use a 2-second output cycle time. If you want to run relays, similar controllers are available to suit.
The Auber SYL2352P (also for SSR) seems highly regarded on your side of the pond. I have not tried it because Auber have no UK presence.
All 3 of these suppliers have excellent technical support. If you need to ask about controllers, it’s pretty fair to assume that not having access to tech support in your own language/country would be unwise.
I use Mineral-Insulated typeN thermocouples for kilns and I usually buy transition-junction assemblies to eliminate any chance of lousing up the wiring. Others have been happy with exposed-junction typeK thermocouples. I would strongly recommend a few minutes on the telephone with coffee, a notebook and a pen, spent talking to the technical sales folk at Omega: they are about the biggest name in temperature measurement and control and give good advice.
No industrial ramp/soak controller will ever approach the user-friendliness of a big-name kiln controller, which will be specifically designed to be easy for the non-technical user. Download and read the manual before deciding on any controller. You may also find it’s worth checking out YouTube for demos/reviews.