Hi and welcome!
As the others have suggested, you do have to be careful using "features" to determine the model (TR2, TR3, TR3A), as when there were model changes, there was some overlap. The commission (TS00000) number is the key, unless as mentioned, some nefarious previous owner has messed with the plate. Bill Piggott's book, "Original Triumph TR2/3/3A" is the bible to all the models and changes, but it's not 100% accurate. What inaccuracies there are I consider minor and a result of later, more complete research. The book was published in 1998, thus out of print, but used copies can be found on the internet. Don't pay too high a price for it, though. I got my copy on eBay, and it was originally belong to the Warwickshire County library!
Part of the problem is that Triumph was not adverse to saving (and thus making) a dollar/pound, so sometimes inventory was used up over a change point in production, confusing the issue for us owners 60 plus years later. So a late TR2 would share many items with an early TR3, sometimes months past the supposed change.
I encourage you to mine this forum, along with another, Triumph Experience at
https://www.triumphexp.com/phorum/list.php?6
Since you're in the UK, you may already be a member of the TR Register and their forum. I always enjoy the different points of view, especially across the pond. Since you're about to embark on a restoration, I highly encourage you to read through or download John Durant's (CJD) several threads documenting the restoration of his 1955 TR2. They're a goldmine of information and can be found here:
https://www.britishcarforum.com/bcf/search.php?searchid=1866123
The various threads of interest are "Beginning the TR2 Bodywork," "Recipe for a TR2," and others. I like John's dry sense of humor mixed with the right photos (that we all like to see) and info that shows his attention to detail and explanation of techniques. The forums have many knowledgeable people that are quite willing to share a wealth of knowledge. Almost every TR question can be answered on these three forums. (Though folks keep trying, no one has yet to stump Randall Young.) :smile-new:
Good luck with the restoration and please, share it with us!