You can't interline within the same airline , since by definition interline is between 2 airlines

You can check bnaggage through on BA as long as the flights are part of the same booking; choose to make 2 bookings and you get the benefits of 2 bookings together with the drawbacks

Would it not have made sense to book an award from LIN-MEX and so avoid having to pay £172 UK APD and reduced the fare disguised as taxes from £100.50 to £46