This looks the same as the deal that The Times was pushing a few weeks ago, so perhaps they were using Acromas (the tour operator behind this) too.
A random search again suggests that this may not be a promo for savvy FTers though
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Taking a 5 night stay at The Rock in Gibraltar as an example, out on 22/6 and back on 27/6, the AA price is £599pp including a free upgrade to Club Europe.
Precisely the same trip, booked on ba.com with Club Europe flights selected from the outset is..... £512pp.
There's nothing to suggest that the AA package wouldn't attract full Avios and TPs, but the BA package definitely does. And, if you're logged in to your EC account when you make a ba.com booking, then you'll earn bonus Avios for buying a package, and up to 3 Avios/£ if you use a BA AmEx Prem Plus card.
There may of course be examples of the AA being cheaper, but as always it pays to check......