Yes, in your case the catering for Cancun to the UK is provided for in Mexico, so pre-order doesn't work. It easier to do from London when there are only a limited number of providers.

If you enjoy beef which isn't incinerated then you best avoid it. BA can do medium rare, but it is so hit and miss that if pre-ordering I would go for the chicken. The alternative is not to pre-order and see if you can get good vibes from the cabin crew onboard about how they will do this for you. Having said that, being on the older 777 from LGW would not give me much confidence of success.