I might suggest a slight retitling of the thread to include the non-US-based nature of the question. You might get some more focused responses from other members who have been in the same boat who might otherwise assume your question is just seeking the basic stuff that is general knowledge on this board.
To try to answer your question, it appears that the AAdvantage Shopping Mall is one of those items not available to AA members outside of the US. I just switched my AA home page to the UK site and do not see an equivalent. I know that a version of the BA Miles eStore is visible on the US website although from the merchants included on that site, I'm guessing it's a store created for Americans that would be separate from the eStore visible to those in the UK.
There were a few options offered. Have you booked rooms for your August trip yet? There is an offer of 2 miles earned for every pound spent on hotels booked through AA's UK site. Same with rental cars. It appears you could also buy miles--although when I clicked that link from the UK page, I was directed to the same page I see when I click from the US site.
Questions such as this really open up my eyes to the varying ways one company does business in so many different countries.