Professional composts are made to a higher standard, with better ingredients, more nutrients, and are not usually available to the public. Many professional composts are custom mixes, and many custom mixes are trade secrets. If you by a lorry load of professional compost (which is the minimum they will make for you) you will pay about £60 - £100 a cubic metre, which is about £5-£10 an 80L bag TRADE price +VAT. And yes, it should be peat based. Very few professional growers would mess about with green waste, a complete waste of time for them.
SO i would doubt very much this is real 'professional' compost, because ASDA would have to sell it at around £6 - £11 + VAT a bag. Ill go and have a look.