Britain's only Green council administration – in Brighton and Hove – is to take the bold step of trying to stage a referendum to see if there is consent among local people for a council tax rise of 4.75%.

Councils are required by law to hold a referendum if they wish to increase the council tax above a government-imposed threshold, currently 2%.

The Green leadership wants to use the extra money to fund adult social care services, including care for the elderly, and grants to third-sector organisations.

The Greens are a minority administration and would need either the abstention or support of either Tory or Labour councillors to push the referendum through.

The communities secretary, Eric Pickles, has often urged councils to stage referendums to test local opinion, rather than "dodge democracy" by spending right up to the government-imposed threshold.

The referendum plan, announced on Thursday by the Green council leader, Jason Kitcat, was a unanimous decision of Green councillors and has the full support of the only Green MP, Caroline Lucas, the South East Green MEP, Keith Taylor, and the Green party leader, Natalie Bennett. The referendum would be held at the same time as the European parliament elections in May.

The local Labour party has been hugely critical of the Greens in Brighton.

Pickles is paving the way to restrict councils to a rise of 1.5% or less, on top of the large cuts already announced. Three-quarters of county councils and a third of other councils have already indicated that they plan to increase council tax to meet growing need and mitigate the worst of Westminster's cuts.

Justifying the move, Kitcat said: "The coalition's cuts mean we cannot deliver the services we were elected to provide and which our consciences say we should provide. We have no choice but to seek the views of local people on funding these services through a tax increase.

"Westminster's ideologically driven cuts to local councils are huge and relentless while demand for our services continues to grow. Vulnerable people who depend on our services are being threatened from Westminster like never before.

"We have so far been successful in saving tens of millions of pounds but we can no longer find enough efficiencies to absorb all the cuts. Without today's proposal, I fear for the serious impacts on the most vulnerable in our city from the coalition's cuts."

Lucas said: "This is a bold move and one that I know the council is taking very reluctantly. The people have not voted for austerity. They have not chosen to have services they rely on destroyed by draconian cuts.

"This is an appalling situation, for which the coalition government is alone to blame. A referendum would allow the people of Brighton and Hove, including my constituents in Brighton Pavilion, to decide on the best response."

Bennett said: "As Greens we believe that decisions should be made closest to the people who are affected. Instead of letting Whitehall impose cuts on vulnerable people in Brighton and Hove, this announcement takes the decision to the people.

"It reflects Green principles being campaigned for around the country. Our Oxfordshire county councillors, in opposition, last year made a bid for a 3.5% rise to protect social care, and I know other local parties will be putting forward similar proposals this year."

The referendum call will be put to the council in February unless opposed by Labour and Tory councillors.

Urging the other parties to let local people decide the fate of local services, Kitcat said: "The other parties, especially Labour, will need to decide whether they trust the people of Brighton and Hove to make this decision. The Green administration I lead did not seek an election mandate to raise taxes in this way and in previous years I have opposed going down this route. But the unprecedented pressure on our budget from Westminster can no longer be absorbed, so we are seeking a democratic opinion from local residents – those who pay council tax and those who rely on the services it funds.

"Westminster is threatening services for the elderly, who have worked hard all their lives and deserve our support in their old age – not reductions in the services which are often a lifeline for them. The city's charities, social enterprises and not-for-profit organisations provide essential services across our city's communities. We must be able to support them."

The Greens say a higher council tax will allow the council to protect "service delivery for key adult social care services, including home care, residential community care, day services, and learning disabilities employment support".

A 4.75% council tax increase would raise £2.75m more than December's draft budget, which assumed a 2% tax increase. A 4.75% increase would mean a rise for a band C property of £5.30 a month and for a band D property of £5.97. Those claiming council tax reduction would still be protected by the existing scheme.

The referendum would cost just over £100,000.