If you click through from Gate 365 to the vendors that BA have listed, such as Apple, John Lewis, M&S, Selfridges and ASOS, you can benefit from significant Avios boosts, sometimes up to 25 additional Avios for every £1 spent.
Note that you don’t get Avios on the VAT element of your online purchases (it's in the small print somewhere, but very hard to find).
As an example, if you click through to John Lewis (currently on a 4 times bonus) and spend £120 (of which £20 is VAT) you get 400 bonus Avios. If you use your BA Black card to make the purchase you also get your standard 1.5 Avios per £1 spent (including the VAT), so 180 Avios. In total you therefore get 580 Avios.
Most vendors allow you to purchase online and pick-up in store within an hour.