The Conservative and Liberal Democrat groups, in opposition in Birmingham for the first time in eight years, have branded a new Cabinet introduced by Sir Albert Bore this week as “unclear” and “lacking accountability”.

The shake-up has seen powers for areas such as housing, refuse collection, parks and leisure centres devolved to the districts and the old cabinet positions leisure, sport and culture, housing, finance and transport and regeneration replaced with a list of new titles and roles.

Now Sir Albert’s eight-strong Labour Cabinet will push agendas and targets for policy areas such as development, jobs and skills, social cohesion and equalities, health and wellbeing and the green, safe and smart city, instead of heading up council departments.

But with much scepticism, cynicism and even confusion as councillors get to grips with the new system, it is perhaps not surprising that shadows from the opposition groups are not identical to the Labour Cabinet.

The Lib Dems, under Paul Tilsley, have created extra positions for spokesmen, with responsibility for covering events in housing, community safety, transport and leisure.

While the Tories, who as the larger of the two opposition groups receive special allowances of about £2,600 per shadow cabinet position per year, have mirrored the Labour group a little more closely – with an additional post for children’s services where they believe that extra political attention is needed.

Tory leader Mike Whitby said he too has been more explicit about the shadow cabinet’s areas of concern, adding apprenticeships and skills to the education agenda and finance and procurement to the commissioning, contracts and performance shadow role.

“The new system is not clear at all,” he said. “There are no clear lines of leadership and accountability.

“It is Sir Albert’s right as the new leader to set up the Cabinet as he sees fit. We’ll have to see how it works out.

“I have told everyone that jobs and employment are key parts of their agenda. Our aim in opposition is not to just dismiss everything Labour put forward but to consider proposals and suggest improvements or changes.

“The test of a good council is – does it balance the budget, work within the budget, deliver service improvement and ultimately customer satisfaction. Under our administration, we saw satisfaction levels rise from 57 per cent to 76 per cent. And it is on those criteria that we will hold Labour to account.”

His leadership has come under fierce criticism from within the party.

He said that although the Tories in Birmingham were on the receiving end of a major defeat at the polls last month, that is partly explained because they did so well in 2008, when many of the lost seats were last up for election and there was a national trend against Conservatives.

He added: “The majority of our councillors know we have a city-wide vision and always have done – and as far as council tax is concerned, we took Birmingham from being one of the highest taxing major cities, to the lowest taxing.

“We are quite confident about growing our base and are focused on regaining power.”

The Liberal Democrats, meanwhile, launched a bid to overturn the new constitution – but this was defeated by the Labour majority.

Coun Paul Tilsley (Lib Dem, Sheldon) said: “On this 40th anniversary of Spaghetti Junction we have a constitution that is our own version. It is over burdened, cumbersome, is not fit for purpose and has no clear lines of account.”

He talked of several cabinet members and committees taking responsibility for housing and leisure, sport and culture – a portfolio he said that when Labour last ran the council was described as a full-time job.

His colleague Jerry Evans (Lib Dem, Springfield) added: “The people of Birmingham said no to an elected mayor, but this new constitution seems to be saying yes. This is the end of cabinet governance.”

Labour leader Sir Albert Bore, while defeating the Lib Dem amendment as a whole, asked them to put the concerns to the council’s business management committee where sensibile suggestions would be considered.