Staff at Department of Social Security offices in Balham and Wandsworth are still on strike due to fears about safety if protective screens are not installed in job centres.
Screens are being removed from Employment Service and Benefit Agency offices as they are merged into single offices called Jobcentre Plus.
A spokesman for the Public and Commercial Services Union (PCS) said: Our members are very concerned about this strike.
We want a negotiated settlement, but until there is adequate protection for our members, strike action will continue.
We are very determined and not prepared to compromise.
He added the union was currently balloting members in Work and Pensions offices throughout Britain if talks were not successful.
The strike, which has been in operation since September 4, meant some residents had claims delayed.
But Maria Powell, 61, of Sarsfield Road, has now received money owing to her.
She said: I got £130 several weeks ago, which was a great relief as I needed specialist shoes because of a fall.
A spokesman for the Department of Work and Pensions said a resolution was possible: Negotiations are ongoing and we are hoping to resolve the situation as soon as possible.
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