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Well isn't it obvious, they want your clay! Must be some fun clay. :p I hope this is a troll post because it's in all honesty it's because Britain is friendly with Mexico. If someone punched your best friend in the face wouldn't you want to punch that person back? Or Girlfriend/boyfriend.
 
LOL, the AI is obsessed with discredits, but they're just wasting 25 influence points when they do that. Be persistent; they'll try to influence lots of countries at once, while you just influence Mexico, and you'll eventually win out.

This. What I do is influence them and let them discredit you, but keep influencing. Once UK has built up enough influence to discredit you again, stop influencing Mexico and they will too. Wait for the discredit to expire and start influencing Mexico again. The UK will immediately discredit you resetting their influence to zero. Again, keep up on the influence to Mexico until UK has enough influence to discredit you again. Lather, rinse, repeat. I've done this a million times to every nation in the game. The only country that it doesn't always work again is France. They are the only ones that I have seen that won't necessarily stop influencing when you do in a given situation.