Such data is gathered by the YouGov surveys, which happen very regularly. Here's the latest report. Unsurprisingly given the sort of policies associated with the coalition government, the approval rating of Parliament splits strongly down party lines. Overall the government is unpopular with a 25% approval rating, 61% disapproval and 14% don't know. However this average disguises the fact that amongst conservative voters approval is 75% and amongst Labour voters approval is only 5%.
These sorts of figures are what you might expect from the UK. The situation is not comparable to the USA where the approval rating of Congress reflects a more deep rooted feeling that corruption is rampant and all the parties are fundamentally the same. This can be seen in the fact that disapproval of Congress is almost identical regardless of voting intention. The problems in the UK reflect a strong north/south division every bit as strong as the city/rural division in the USA, where the richer and more conservative south tends to approval of austerity due to a less systematic dependence on welfare and public sector jobs. The post-industrial north is dominated by Labour voters who never made the transition to the service/knowledge economy and where quality of life is highly dependent on government spending.
I don't have time to find more precise stats, but I suspect if you examined UK voters beliefs more closely, people would not feel that democracy itself was particularly broken. Especially not over something as trivial as piracy - only in places like Slashdot and amongst the people who read it does piracy become some kind of moral imperative. Everyone else I know treats it as a naughty pleasure. They know they're breaking the law and won't get caught, but they don't have any desire to make a big moral campaign of it.