Would a double sheet fit my mattress?

I have a Sealy posturepedic mattress measuring 135 (width) by 190 (length) by 29 (width) cm. I need to buy some sheets for it and am currently looking at Argos but I'm not sure if what they have will fit my mattress since I've already bought a double mattress protector from them and it barely wraps around the bottom edge of the mattress... I think mine must be a bit deeper than standard double mattresses because of the extra foam. So what kind of sheets should I buy? Flat or fitted? Double or maybe something bigger like king? If you don't know the answer, would any of the sales istant at an Argos store be able to help?