TLDR: The Great British Baking Show cooking thermometer is the KitchenCraft Home Made Deluxe Stainless Steel Cooking Thermometer (Amazon Link).
KitchenCraft Home Made Deluxe Stainless Steel Cooking Thermometer
I was not sure what to title this post - jam thermometer, deep frying thermometer, professional thermometer, candy thermometer, or caramel thermometer. I'll call it the same as KitchenCraft. For all their analogue temperature measurements, the bakers on The Great British Baking Show use the KitchenCraft Home Made Deluxe Stainless Steel Cooking Thermometer (Amazon Link).
The bakers use this thermometer a couple times per season, normally when they are making jam, because as they put it, "it has jam on the thermometer."
The KitchenCraft cooking thermometer (Amazon Link) is actually pretty useful. It is an analogue thermometer, which means you read the red bar along the gauge as it increases in temperature (sorry anyone over like... 12?... for the explanation).
This thermometer has quite convenient markings along the gauge to tell you when certain things are ready. In addition to "jam," it has temperature measurements for fruit bottling, sterilize, soft ball, firm ball, hard ball, soft crack, firm crack, caramel, fish, and chips. For those of us in the USA soft crack and firm crack refer to cooking sugar. Phew.
The thermometer is made from stainless steel and "robust" glass in order to function in pots and pans, as well as deep fryers. It is mercury free (good!), can measure temperatures up to 400 F ( ~220 C), and has a built in clip on the back so it can attach to pans.
This is a bit more convenient than the digital thermometers, in that it can be left clipped to the pot or pan as things are heating up. This allows hand free operation instead of having to continually check the temperature with the digital thermometer's probe. However, quite frequently I'll see the bakers opting to do just this, mainly while tempering chocolate.
Owning to the theme of The Great British Baking Show, KitchenCraft is a British Company. They were formed in 1850 by Thomas Plant and bore his name until 1996 when they rebranded in order to more clearly state what they do.
KitchenCraft is part of Lifetime Brands Inc. (US based), a conglomerate with roughly 20 subsidiaries. They make roughly 5,000 different products and can be found nearly everywhere. Most of their manufacturing looks to be done in China, while their products are packaged in other countries. They boast that every kitchen in the UK has something made by them.
Which means if I ever move to the UK, I will specifically not purchase their products so they have to append "*except for..." to their claim.
Every year they win a few awards for excellence in some category, which means some of their kitchenware is a great hit, some of it looks to be ... plastic spoons. So it feels a bit like a mixed bag, in that they are trying to do everything.
However, it does seem like their thermometer is quite iconic. I would also guess that they lost their patent and copyrights on it at some point in time because you can find 30 or so that have the exact same form factor from various other companies, mostly from China, but some even from the UK. The only difference being what markings are on the gauge.
KitchenCraft Gauge Detail
I'm going out on a limb here to assume that the KitchenCraft Home Made Deluxe Stainless Steel Cooking Thermometer (Amazon Link) is the OG cooking thermometer, and thus why there are so many copies of it. I can not find any companies that are older that make this thermometer, and the fact that The Great British Baking Show uses it puts it on top in my mind. It costs less than $20, so if you're in the market for one, go for it!
If you're looking for alternatives this is kind of hilarious... take a look at each of these. I'll even Photoshop them side by side for giggles. You can discern the KitchenCraft because it has the immersion line on it (same as the Tala), but also does not have "China" printed on the front. The prices range roughly 250% of the cheapest one (all still sub $20), but some of the ratings are just deplorable. The stars for dollars award definitely goes to the Taylor cooking thermometer.
The list goes on and on... and on... and on. Identifying the cooking thermometer from The Great British Baking Show was all the harder because of this... just... ugh.