In general, it's fairly difficult to get a funded PhD position in the UK, if you're an international student (as of a few years ago, "international" was defined as non-EU; I assume that has changed now, but I haven't lived in the UK since pre-Brexit).
From what I've seen, an international grad student in the UK basically has a few options, such as: (1) ultra-prestigious scholarships like the Rhodes scholarship, (2) external funding, e.g. from industry or their home country's government (this is common for students from many Asian countries), or (3) compete for a very small number of department or university funded positions/scholarships open to internationals.
This is very different from the situation in the US and most of continental Europe, where a PhD position always comes with a salary, and where there's typically no discrimination between domestic and international applicants.
Are there historical reasons why the UK PhD system is like this? It seems strange, especially given that the UK is a wealthy country strong in scientific research. Why don't they reform their system to better attract international talent?
(My field is physics, but I think the same is true across at least some other STEM subjects.)