This gets tricky! While the battery is available it can’t be shipped by air. So you are limited on where you can get it. As an example in the EU you could get this one [https://www.thebookyard.com/product.php?cPath=39_367_616&products_id=21842|18/19 13” MacBook Pro 13" Battery (4TB ports) Apple P/N 820-01118] and here’s the guide [guide|133172]
If you have a friend traveling to the UK they could pick it up for you as they can hand carry it on the plane.
While you can replace the battery alone, Apple won’t! They only replace the full uppercase which is what the person was trying to tell you as they don’t have a in-house service center. and Apple also requires them to use their parts so that limits them on what they can do. An independent repair outfit is not bound by Apples rules.