Each university has different scholarships, which are highly competitive. My advice is to narrow your university choices and look at the department's webpage (funding tabs are usually within the PhD program information). Potential supervisors also can tell you about the history of funding the in department (for example, the two I ended up applying to told me there was only one intl. funded position out of 20 applicants, but no guarantees for funding next year!) So vary your uni. choices. If you go for a uni. with less competition, you'll get more of a chance for funding, obv.
I do think the US has more funding options than the UK, but PhD program there is typically longer and there's more teaching work. You can also look at programs in Canada. If you have the time, it would not hurt to take the GRE so you can apply to a varied group of unis.