I can't find any evidence of a Blackpool Tomato variety. But there is tomato farming in Blackpool, notably at Blackpool Tomatoes. So Blackpool Tomato seems to be a brand rather than a variety. Locally one could buy one, collect the seed and grow it, whatever it may be. No doubt if you live somewhere like Blackpool, it grows well.

Jersey Tomato has more than one possible meaning. In the US, a Jersey Tomato is a tomato from New Jersey, and the concept of a "real Jersey Tomato" is a bit like "the real McCoy". The particular historical variety they notably used, and now use again, is called Ramapo. It fell out of use, and had to be tracked down, rescued and restored, which may account for the need to identify a real Jersey Tomato as indicated by the saying, as evidently there were a lot that weren't. In the UK, Jersey (and Guernsey) in the Channel Islands grow tomatoes, and market them as "Jersey Tomatoes". They used to grow a lot more, but they still grow a few. A "Jersey Tomato" is certainly a brand, but whether there is a specific variety they use, or whether a Jersey Tomato is just any tomato from Jersey, I have been unable to discover. What you can do is buy one (in season), collect the seed and grow it yourself. As for the ease of doing this, Google suggests it might be hard unless you are going there. I see that all but one of the growers have stopped export to the mainland. But Sainsburys indicated it still plans to sell them.

Personally I'd think it better to research tomato varieties and grow a good one. It looks like you are already doing this.