Every PS2 is region locked. There are several regions, such as region 1, region 2, etc. I'm kinda an idiot I can't even remember which number refers to which region... I think region 1 is US, region 2 is Europe, etc.
Anyways, to the point, like I said every PS2 is region locked. It cannot play content that is from outside of the country/region the PS2 is from.
If you have an American PS2, it will not play Asian or European DVDs. Try putting the DVD onto your laptop, it might have to ask you to switch your region for the DVD to play correctly, it'll list all the regions.
The PS3 is totally region free, as far as I'm aware. PS2 is still old school region locked though, unfortunately. Did not work when I tried to play my Kung Fu Hustle DVD.
It's hard to say based on the way you've phrased the question.
The PS2 will play what is colloquially known as a universal DVD (which basically means that it's a DVD with no region encoding), but it is NOT a universal DVD player (which would mean that it could play any DVD regardless of region encoding).
So if you're buying a DVD that is region encoded for the UK, no, a US PS2 won't play it. If you're buying a DVD from the UK that has no region encoding, then yes, a US PS2 will play it (as will most other DVD players).