Yes, governments declare wars we don't approve of (I'd still fuming if I was American for my government joining in the European part of the 2WW), sign up to policies we can't see the benefit to (Gosh, joining Europe was SUCH a big mistake with its crazy modern notions of gender equality... I'd much rather get fired for being pregnant than being allowed to keep my job) but we are part of a democracy... it may be flawed, because you may have to put up with a decade of government you didn't vote for. Colluding to evade paying tax because you don't like what those taxes are spent on is such a hypocritical argument - if you don't like democracy, try living in Syria...
As several people have pointed out, this is not an argument about paying cash for small jobs - its about agreeing to a 15-20% discount for paying cash, knowing that they will not put it through their books. As want2B points out, you can get discount for cash on the basis that there is no credit risk, and that is an entirely separate matter.
You can always ask your tradesmen if they're VAT registered - remember that if they are, they will not be paying VAT on the goods they provide (so that bath that the plumber installs will be 20% cheaper) so you are already, in theory, getting some discount. If they're not paying VAT on the goods then it is immoral to not collect the VAT in return. Part of being registered for VAT is a "contract" with HMRC - you don't pay VAT in recognition of the fact that you're performing a valuable service in return by collecting it from consumers on their behalf. I'm sure some of Mr Gauke's remarks (which were in response to a direct question on the issue) were intended for the plumbers, builders etc who offer "cash in hand" discounts of 20% (as opposed to "cash discounts" of 5%).
The flip side to the argument is that the grey economy does play a vitally important role in the country - by paying your cleaner cash that she doesn't declare, she has a bit more money each month. If you forced her (or him - sorry, didn't mean to be sexist!) to declare her earnings, I'm sure you'd get to a tipping point where she either decided it wasn't worth taking on that job, or putting her prices up to the point where you decided you couldn't afford her, thereby stifling economic activity.
Oh yes, and whoever said that taxes never go down, does that mean you're still paying income tax at 90%??