Your chances of it working are somewhere between slim and none.
The vast majority of discs sold in the UK are region 2 and will say [2] somewhere on the disc / packaging. Some are region 0 (ie, will play on any player) but these tend to be things other than movies / TV shows. Music videos, kids’ shows, documentaries, that sort of thing.
Multi-region DVD players are relatively common in the UK, due to the ubiquity of American movies. The same is not true in the US, you will be hard pressed to find a player that isn’t region 1 locked.
You could rip them, but then you’ve got the small issue of taking pirated DVDs through customs. If I were you, I’d probably take a laptop with me that had a DVD player in it.