I don't know where you booked your ticket, and under what country's laws... my understanding is that under UK law airlines are supposed to refund taxes, though there are some that won't. Ryanair have it in their terms and conditions that they won't. Some airlines refund taxes in theory, but then charge an administration charge which leaves you with nothing.

My partner cancelled a non-refundable KLM ticket last year and got the tax back without any problem.