The APD may be lessened if you travel between the UK and Mexico via a European hub city (Amsterdam i

The 2012 British fiscal budget increased the "Air Passenger Duty" (APD) on flights between London and Mexico by around US$10, from £75 (US$120) to £81 (US$130)— per person .  This is for economy class; if you travel premium economy, business, or first class, the rates will rise from £150 ($240) to £162 ($260) per person.  APD is a form of "departure tax", which is added by airlines to your total air ticket price and paid over to the UK government.
The APD may be lessened if you travel between the UK and Mexico via a European hub city (Amsterdam is ideal as the Dutch don't charge departure taxes), because the APD on your flight american airline flights out of the UK would be charged at the much lower rate of £13 ($21), or £26 (US$42) for premium-class travel.  However, you must purchase the long-haul ticket separately because if your itinerary out of London american airline flights shows your final destination as Mexico, you will be charged the higher american airline flights rate, even if you travel through Europe . For example, instead of buying american airline flights a ticket to Mexico City from London connecting through Amsterdam, purchase a round-trip ticket to Amsterdam and then purchase a separate round-trip ticket from Amsterdam to Mexico City.
Avoiding excessive APD tax requires some additional research and the purchase of separate tickets (and the savings will also be subject to flight prices) but it only takes a few minutes to compare prices online and the sums involved could make the additional few minutes of planning worthwhile.
Choosing option C can deliver tax savings totaling at least US$436 ($109 per passenger). If your family travels in premium economy, business or first (or you are upgraded using air miles) your costs or savings are doubled.
British Airways connects London and Mexico City on direct flights, several days a week; KLM connects Amsterdam and Mexico City daily.  There are frequent daily connections between Amsterdam and several UK cities.