It follows attacks on Mr Miliband by the leaders of the GMB and Unite.
Fourteen Devon construction workers were on an industry blacklist, the GMB union has claimed.
Gary Smith, from the GMB union, said it was "bad news for the economy".
Paul Kenny, of the GMB union, called it a "significant day for UK workers".
After a meeting in Dundee, GMB shop stewards have recommended that its members reject the proposals.
The industrial action is being taken by members of the GMB and Unite unions.
The GMB asked for donations to be sent to the Appledore Shipbuilders Welfare Club.
BBC: NEWS | UK | England | Devon | Financial help 'floods' into shipyard
Last week members of the GMB union rejected a new offer from management in a ballot.
The GMB union says losing lock keepers could lead to a slower response time and possible flooding.
Mae'r bil arfaethedig wedi ei gefnogi gan Trades Union Congress Cymru, ac undebau llafur Unite a'r GMB.
The GMB union said the UK had fallen 20 places behind in an international gender pay league.
Both Unison and the GMB have said they are not in a position to sign the deal.
Paul Wade from the GMB union said members would be balloted when the final proposal was confirmed.
The GMB and Unite unions said its members were planning a second strike for Thursday 26 July.
BBC: Remploy staff in Coventry join strikes on factory closures
The GMB said nearly half of Remploy's 54 factories in the UK have already been shut down.
The GMB union said it knew of at least three different parties interested in buying the yard.
BBC: NEWS | UK | England | Devon | Financial help 'floods' into shipyard
Colin Todd, regional officer for GMB, said it was promising that the service appeared to be listening.
It claims a part-time post of GMB's union convenor, employed by the council, is also under threat.
The GMB union has said its members in the council's Cityclean department are being balloted for industrial action.
But Colin Todd, of the GMB union, said they would continue to fight plans to close ambulance stations.
BBC: New East Midlands Ambulance Service plan to go before board
The GMB union said it was pleased it appeared to be listening but said the changes were unnecessary.
Members of Unison, Unite, the GMB and the construction workers union Ucatt are taking part in the strike.
GMB's Stuart Fegan said he was concerned the plans could have a negative effect on the lives of staff.
Those words were welcomed as a "significant change in tone" by John Edmonds, general secretary of the GMB union.
The other four unions Mr Maude said had agreed to the deal were Prospect, FDA, Unite and the GMB.
Members of the GMB and Unite unions will walk out from 28 August.
Union leaders from the GMB, TGWU and Amicus are examining the new BA proposal, and have yet to comment.
But Charles Harrity, GMB senior organiser, said the dispute was over "plans to make huge cuts to their take-home pay".
The GMB union, which represents the workers, called the decision a disgrace and said the council was threatening children's safety.
According to GMB, Glasgow had the biggest number of blacklisted workers - 138 - followed by Edinburgh, which had 52.
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