The 17 bishops include John Arnold, Auxiliary Bishop of Westminster, and William Kenney, Auxiliary Bishop of Birmingham.
They estimate that corporate secrecy and tax dodging is depriving the world's poorest countries of more than £100 billion a year.
They are calling for rules to "put more morality into the financial system" and stop multinational corporations from shifting profits to tax havens where they pay little or no tax.
"The greed of a few threatens the very survival of the most vulnerable populations," the bishops said.
"To end this, new rules are urgently needed that ensure that the wealth produced, particularly from the exploitation of natural resources, is not monopolised for the sole benefit of a minority.
"These resources should benefit all equitably and in particular the local people who are directly impacted by the activities of production or extraction."
The bishops say that country-by-country reporting would force tax dodging companies to break down their results for each country they operate in and help poor nations identify and collect the taxes they are due.
The bishops add that improved transparency would also strengthen democracy.
"It is now up to the European Union to improve the international standard of transparency," they said.
"The Commission has proposed a rule for financial transparency, on both a country by country and project by project basis. If implemented effectively, these measures will offer more opportunities to citizens to monitor whether extractive industries are making a fair contribution to the economy.
"To achieve this goal, the European Union must ensure the threshold for reporting payments by extractive companies is set at a level that is meaningful for developing countries. Exemptions should not be allowed to create loopholes."
Christian Aid’s economic justice advisor Joseph Stead backed the bishops’ call for better regulation.
He said: "If developing countries are to be able to raise the revenue to pull themselves out of poverty and reduce dependency on aid they need to be able to collect the tax owed to them, including by rich corporations.
"We all have a moral responsibility to hold these companies to account and it is important that lawmakers play their part and introduce legislation which helps to end tax dodging."