For the most part, it's not U.K. "taxes" (properly so-called) as much as it is BA "carrier surcharges" that you are seeing. Using BA Avios to book award travel on Iberia -- when available -- is a decent option for trans-Atlantic travel.

For booking travel on AA within the Americas (North and South), using Avios is an option when there is Avios availability, but:

1. BA charges for each flight flown, so if you have to make a connection somewhere, the value you get from your Avios will be diminished;

2. BA often has trouble displaying AA award availability involving connections;

3. AA has recently revamped its rewards structure by eliminating MileSAAver awards, and going to fully-dynamic award pricing on AA flights. We're still learning what the criteria are for when AA award flights will be available for redemption by partner programs.

Note that an award itinerary involving two or more BA partners -- such as AA and AS -- will price based on BA's multi-carrier award redemption scheme, which only considers the total flown mileage of the entire itinerary, rather than charging for each flight separately. This can result in paying more, or fewer, Avios for the trip, compared to bring charged for each segment individually. BA multi-carrier redemption rates here:

https://www.britishairways.com/trave...e/public/en_us