The GDP calculation measures our economic activity. It should not be censored or bits omitted because they may not be pretty. The fact is £10billion worth of transactions take place in the black economy, and to not measure them does not reflect the true level of prosperity in this country.
I could equally object to money made in the city dealing in commodities such as mining in third world countries should be omitted. Thousands die every year extracting these minerals for a pittance of a wage, and then trades made in the City of London earn £millions to our GDP. Not sure that is any worse, but you wouldn't get the Daily Mail and its supporters saying profits made from trades with the third world should be omitted.
The main thing is we get true, accurate and reluable figures produced, even if that includes some dubious activity.