The tax, also known as the “Robin Hood tax”, falls on all financial exchanges, including shares and bonds.
It has already been adopted in other European countries, and County Coun Gina Dowding called on elected members to support the move.
Speaking at the full council meeting at County Hall, the Green Party representative said the tax would ensure the number of high risk financial transactions were curtailed, and would start to “rebalance” the economy.
She said: “By passing this motion in this chamber, we are sending a clear message to the government that we want a financial system that works for the common good of ordinary people and not for the vested interests of the few.”
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It is said that at the rate of 0.05 per cent, the tax could raise up to £250bn per year globally and up to £20bn per year nationally.
Councillors voted by majority to ask to write to the Chancellor of the Exchequer and the Secretary of State for communities and local government to adopt the financial transaction tax.
The move follows a decision by councillors on Preston Council to ask the chief executive to write to national leaders and Preston MPs in support of the tax, following a call from Coun John Browne.
County Coun David Borrow said: “Where we are now is a society where division in terms of income and wealth is getting wider and wider. The gap between the rich and the poor is widening - you see those at the top grabbing a bigger chunk of the income available and the people at the bottom seeing their income slow down.”
He added: “I hope that council will support this resolution on the basis of becoming a fairer and more equal society.”
County Coun Graham Gooch said: “We should have nothing to do with this motion and we should reject it.”