They include how many guns and knives are taken off the streets every year, how many rape suspects are charged and convicted, and how much money is lost to fraud.
The letter - seen by HuffPost UK - has been sent to the top civil servants in the Home Office, Ministry of Justice and the attorney general’s office.
It comes amid the government’s so-called “crime week”, which is aimed at showing the Conservatives are the party of law and order as the next general election looms.
But the Labour letter dismisses it as “the usual dribble of announcements designed to create headlines but not make any actual difference to the breakdown of law and order in our society”.
Thornberry, the shadow attorney general, adds: “I do not want to drag you or your civil service colleagues into that debate, but it has illustrated once again the enormous gap between the rhetoric on crime and justice that we hear from ministers, and the reality that the rest of us see every day on our streets and in our courts.
“Our efforts to establish even the most basic of facts have hit brick walls [with] ministers not just unwilling but unable to say whether their results are getting better or worse.”
She adds: “It is always striking to note the lack of concern [from ministers] over such glaring gaps in the government’s knowledge, and their apparent willingness to let them persist.
“There appears to be an attitude amongst ministers of ‘what I don’t know can’t hurt me’, or more properly put, ‘what people can’t prove, they can’t criticise’.”
Labour says there needs to be a “change in culture, which says that the public has a right to know this information, and that – even more obviously – ministers should want to know it too”.
Other areas where Labour say the government is failing to provide vital information are the extent of court backlogs and how many migrants who arrive in the UK via small boats have absconded from hotels.
A government spokesperson said: “We publish a wide range of data to bolster transparency and public confidence in the criminal justice system.
“According to the Crime Survey for England and Wales, violent crime has fallen by 46% and neighbourhood crime is down 51% since 2010.
“This government is committed to bearing down on crime, recruiting an additional 20,000 police officers for forces in England and Wales who have committed to pursuing all reasonable leads to catch perpetrators.”