Will UK Nintendo Wii games work on a US Nintendo Wii?

No, The two types of consoles have different region encoding.

This is called Region Lockout (or Region Lock).

They are incompatible. UK games will not work on a US wii. The UK use a PAL (Phase Alternating Line) system whereas the US use NTSC (National Television System Committee). There is a CD called Freeloader which should allow you to play games from different regions on your US wii. i.e JP and UK games will work on the US wii with the CD