Union officials have told national negotiators it is now their turn to move, as they hail major strike action over public sector worker pay and pensions a “success”.

Trade union officials have said it is time “to put up or shut up” in their dispute over public sector pay and have called on Local Government Association negotiators to accept an offer of arbitration to resolve the issue.

And they have warned an “escalation” of today’s is likely later in the year if the strikes do not force changes.

More than 3,000 people took part in the protest through Brighton and Hove yesterday, walking from Hollingdean depot and Hove Town Hall to The Level while thousands of striking teachers, firefighters, council employees and government workers refused to work across the county.

Brighton and Hove saw the most disruption to services, compared to very minimal disturbances elsewhere in Sussex.

City residents had no bin collections, the Royal Pavilion and Brighton Museum and Art Gallery closed and a number of libraries kept their doors locked.

The Argus understands that half of all non-school staff at the council were on strike.

Pupils at almost 200 schools across the county had the day off because of full or partial closures, claimants visiting Brighton Jobcentre in Edward Street were told to come back today and almost all Public and Commercial Services union members went on strike.

The march itself caused some disruption as the parade walked along one carriage of city centre roads and Brighton and Hove buses reported disruption on most services.

The action in Brighton and Hove was among the biggest gatherings in the country which saw more than a million workers nationwide down tools in the largest one-day strike over pay by public sector employees since 2010.

GMB branch secretary Mark Turner said the day was “very positive” despite turnout falling short of anticipated figures.

He said: “We will consider our next move in the next couple of weeks but there is no doubt they would have heard us in Bournemouth where the Local Government Association is having its conference.

“This is the first step in the shape of things to come so we would urge them to take up our offer of going into arbitration with Acas.

“The public sector is very, very angry, just look at how many schools were closed in Brighton and Hove.

“These people are having to take second jobs, they are living hand-to-mouth and they have seen their pay go down over the past five years.

“This is not a dispute with the local authority but we would call on the chief executive and the council leader to put more pressure on their negotiators to get round the table.”

Phil Clarke, secretary of the Brighton and Hove Trades Union Council, said: “Without a doubt the action has been effective and sends a very clear message to the Government that it is not acceptable that the public sector has seen a decade of pay cuts.

“This has to stop and we have to be valued for the work we do.

“The support from the public was brilliant, a lot of people were coming out on to the pavements and applauding the march, parents who had to take the day off to look after children were cheering and applauding. In my opinion if the Government does not back down, you will see not just a repeat of this but an escalation.”

Simon Herbert, East Sussex chairman of the Fire Brigade Union, said spirits remained high among members, despite taking part in more than a dozen strikes over the year with no end in sight in the pensions’ dispute.

He said: “It is a danger that fatigue could set in on such a long dispute but the determination and strength of feeling among the members is just as strong if not stronger than when we first went out.

“We are losing money every day we go on strike and our members are amazed that fire services minister Brandon Lewis has not moved on his position.

“We are prepared that this could drag on and we are not going anywhere.

“It may be a political game for Mr Lewis but we are fighting for our futures.”

Conservative councillors in Brighton were critical of the strike action, questioning its mandate and concerned about the impact on residents.

Group leader Geoffrey Theobald said: “The low turnout for the march reflects the lack of mandate for this action - just 8.3% of Unison members voted to support a strike.

“This makes it very hard for the unions to justify the disruption and inconvenience they have caused residents.

“Today’s rubbish collections for example will not now take place until next Thursday which will no doubt have knock-on effects and many communal bins will be overflowing.

“I commend the schools in the city that managed to stay open today, including the two academies, BACA and PACA, but for those that didn’t, it is disappointing that their pupils have lost a valuable day’s schooling and that many parents will have to have taken a day off work.”

Brighton Pavilion MP Caroline Lucas was one of a number of speakers at the gathering at The Level alongside Labour candidate for Brighton Kemptown Nancy Platts, Hove Park School NUT rep Liz Ritson and GMB officials.

Ms Lucas said: “It is very clear that austerity isn't working.

“Strike action is the option of last resort and the decision to take part will not have been taken lightly.

“It is simply unacceptable that workers continue to suffer pay cuts and freezes and I’ll continue to lobby the Government to do the right thing by increasing public sector pay.”

Labour group leader Warren Morgan was among several Labour and Green city councillors who joined in the march.

He said: “I think we’re in a huge crisis, with a large number of people in jobs we all rely on not being able to keep up with the cost of living, so I’m here to support those people.”

Tom Scanlon, director of public health at Brighton and Hove City Council said: “We made sure we had done as much preparation as possible and had contingency plans in place.

“Essential services which look after vulnerable adults and children in our city were protected and exempted from the strike.”