Buy some loquats at a fruit market (Chinese-owned would probably be best chance of finding them), eat the loquats, and grow the seeds. That's how I did it.

Note that Loquats (the tree) are hardy in much of Britain, but the summers here aren't warm enough for fruit production, you'll only be able to grow it as a foliage plant.

Resin

I'm sure there are one or two cultivars that would do much better at fruiting here but I don't have the names. One think worth knowing about Loquat plants is the more shade they get, the longer the leaves will be, over a meter long in extreme cases if I'm not mistaken. Whether this applies to the sun challenged UK is another matter, I think they need what sun they can get. I have one grown from seed that's shaded a lot of the day, it hasn't shown much growth in 3 years and has yet to appear this spring. I think it's a good option to grow them in large pots so you can move them if needed.

Eriobotrya is an interesting plant. I used to think it was a citrus but its actually in the rose family!
There's a guy over on the european palm society site offering up seedlings for exchange.

Here is a link that might be useful: EPS

It might not be just the cool summers in Britain that prevent loquats from fruiting. Our summers here in Jackson, Mississippi, are terribly hot and humid (with average highs of 92F [33.3C] June through August). The loquats flower in November, but the flowers or fruit are usually killed by freezes (our first frost is usually around late November). We have acidic clay soil. The trees seem to thrive in our heat and are fairly common landscape plants.

I've seen fruiting trees here in south London.