US Nintendo DS Games on UK Consoles: Region Compatibility Explained
Yes, they work. The original Nintendo DS and DS Lite are region-free for DS game cards. A US cartridge plays perfectly on a UK DS or DS Lite.
The Important Exceptions
DSi-enhanced / DSi-exclusive games (black cartridges with white border) are region-locked on DSi, DSi XL, and 3DS family systems. They will run in DS mode on original DS/DS Lite without any lock.
Online services (defunct). Nintendo Wi-Fi Connection segregated regions; some games blocked cross-region matchmaking. Irrelevant now that servers are offline.
Bottom Line
For 95% of the DS library on original DS or DS Lite hardware: fully compatible, no issues. Import away.