Identifying a cherry variety

Hi everyone, I'm new to the forum, though previously a lurker.

In the house we had prior to our current one there was a cherry tree. It was there before we moved in so I don't know what variety it was and, since I'm redesigning our current garden I'd like to have the same variety. The reason being, I'm not a huge fan of cherries but this tree produced the most amazing fruits I've ever eaten. They were fit to bursting with juice and turned your hands blood red when pitting them. The flavour was rich and strong with an almost sherbet-like tang to it. They were unlike anything I've ever had and would love to have ready access to them again. When I've spoken to people about it, the tanginess has led them to suggest it would be a sour variety, and they may be right, but the flavour was not what I would describe as sour, personally.

So I was hoping someone might be able to help me with identification, but what would you even need to successfully identify it? I no longer have access to the tree, but I can photograph it from over the wall, and could probably ask the current owner for a sample if a photograph wasn't enough (though they may say no!)

If anyone would be willing to help, please do let me know.