Does the distance from the equator have an effect? For instance a far higher proportion of Mexico's birds recorded this year have already been recorded than Britain's?
All the best
Yes...the latitudinal diversity gradient, which operates with most taxonomic groups, not just birds.
Its a bit less clear what drives it, but one theory is it is essentially to do with greater ability to specialise in a less seasonally varied environment. There's also less reason to migrate, and any sort of isolation of habitat can lead to speciation over relatively small geographic areas (e.g. antpittas in eastern / central / western Andes ranges). As far as birds are concerned, those species which do migrate into the tropics then add further to the country's list.
Mexico will have a lot of wintering species from North America, but rather fewer summer visitors from further south, so it'll be easier to build up a big list early in the year.