Using two keyboards with different layouts simultaneously

I am using a MacBook with a UK keyboard layout and a USB keyboard also with a UK layout. However, some of the keys are assigned differently on the two keyboards. For example,

Shift-2 is @ on one keyboard, and " on the other. The key to the left of 1 (key code 10) is §/± on one keyboard, `/¬ on the other. Etc.

I have created two .keylayout files, one for each keyboard. Each .keylayout works correctly with the keyboard it was created for, but if I activate one .keylayout, one keyboard works correctly, and the other works incorrectly, and vice versa.

Is there a way to set the MacBook up so that both keyboards work correctly at the same time - i.e. that the key displaying @ on either keyboard sends through @ rather than " etc.?