I mostly use T&M. I used to buy from T&M a long time ago when they were the only company to offer a book-sized colour catalogue. I have used Chilterns Seeds, which is a small company who stock some of the more obscure varieties. Their catalogue has no pretty pictures in it, so is not very useful for browsing. And I have used a few others.
With many varieties of seeds, it's likely that the seeds are produced by a grower who specialises in that type of plant, and he distributes his seeds to many commercial seed suppliers worldwide. In such cases it doesn't matter a jot which company you buy the seeds from because they all originate from the same grower.
If you read the fine print on the back of a seed packet it may tell you the country of origin. It's often on the back, right at the top - the strip that you rip off to open the packet. I've just glanced at a few packets I have at hand - many are from Holland, some sweet peas and gazanias come from the USA, calendulas from Poland, astranta from Germany, foxgloves are from Holland, Spain and Portugal. And those packets of seed are all sold by T&M.
I don't think that very much flower seed actually comes from nurseries owned by seed companies in this country. I haven't inspected any packets of vegetable seeds and don't know where most of them come from. It might be interesting to find out.