The government's mooted tax on City law firms is just one of several options for improving the UK court system under consideration by government, senior partners in the City were told at a series of meetings with justice secretary Michael Gove earlier this week.

Lord Chancellor Gove met with senior partners from top city firms twice this week to discuss how the legal elite could make further strides in making justice more accessible.

The meetings followed news last week that Gove was considering introducing a tax on the UK's largest law firms as a way of offsetting revenue the exchequer will lose from a separate plan to abolish controversial charges for defendants in the criminal courts.

Gove, Ministry of Justice officials, City of London Law Society leaders, and senior partners and pro bono specialists from a selection of top City law firms met at Clifford Chance's offices on Monday to discuss how firms could make a greater contribution to the publicly-funded legal sector.

Then on Wednesday evening, partners from City firms are understood to have attended an annual dinner hosted by Gove and the City of London Solicitors Company at Guildhall.

City of London Law Society chairman, Alasdair Douglas said: "Many ideas were floated, of which a tax or levy, voluntary or imposed, was only one. Our response to the Lord Chancellor's challenge remains a work in progress and we are keen to work constructively with his department."

Douglas added that demand for free legal advice was "insatiable" and any expansion of City firms' prop bono work had to be balanced with "the provision of pro bono in the other jurisdictions where our members work, and the need to compete successfully in the international legal marketplace".

He said: "Domestic pro bono support will never be an adequate substitute for a publicly-funded legal aid system."

A spokesperson for the Ministry of Justice said the justice secretary found the talks "useful".

He added: "As well as discussing pro bono and investing in access to justice, the Lord Chancellor took the opportunity to offer his practical support for the continuing international growth of UK law firms."

Gove has long been opposed to what he has called the UK's developing "two nation justice system".

In a speech in June he said: "While those with money can secure the finest legal provision in the world, the reality in our courts for many of our citizens is that the justice system is failing them."

He added: "I believe that more could – and should – be done by the most successful in the legal profession to help protect access to justice for all."

But the plan to tax City law firms that emerged last week was meet with bafflement and indignation among the sector's leaders.

Senior partners have said it is difficult to see how such a tax would work and Law Society president Jonathan Smithers slammed the plans as a "tax on success".

He warned such a tax could "prompt firms to consider whether to continue to operate out of England and Wales", which he argued would "have an impact on the wider UK economy".