I don't know about AS, but BA certainly charges (in common with most European airlines) a myriad of fees and surcharges on top of the ticket price itself. These are also applied to award tickets.

The only actual 'tax' is a departure tax (£5 shorthaul/£20 longhaul, double for premium classes). British airports also charge a passenger service charge of about £7-£10 for each departing passenger.

The current BA fuel surcharge is £30 for a longhaul sector, £8 for shorthaul.