Hopes for a breakthrough in the month-long strike on South Western Railway have been raised after the RMT union issued a plan to resolve the dispute.

The train operator welcomed the move but cautioned that there was no formal offer of talks.

The strike, due to last 27 working days across December, entered its second week on Monday, spelling more misery for passengers on Britain’s second-busiest rail network.

Hundreds of thousands of commuters on SWR have been struggling with disruption that has resulted in more than 40% of normal services being axed from the schedule. Trains that are running have been even busier than usual, with passengers held outside some stations to queue at peak times.

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The last direct talks in the long-running row over the role and responsibilities of guards broke down without agreement in November. The RMT said its “six-point road map to a settlement” would guarantee to retain guards in an active, safety-critical role but acknowledged that it could prolong the time a train stops at each station.

Its general secretary, Mick Cash, said: “We are literally three seconds away from a deal that would achieve both our objectives and the company’s.”

An SWR spokesperson welcomed the RMT’s move but said the company needed to understand what was new or different in the plan. He added: “We actually agree with most of the RMT’s points but on a busy metro network like ours every second counts and we cannot have unnecessary and inefficient practices that increase delays for passengers.

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“The best and safest way to operate the new trains we will introduce next year is with the driver closing the doors, as the industry’s own safety body, the RSSB, has said. Only by doing this can we free up guards to offer the customer assistance the RMT describes, making our trains more accessible and providing better customer service to everyone.”

Cash said SWR’s response should open the way for detailed talks at Acas and he confirmed that the union was prepared to call off the strike. “If the company can give us an assurance that they accept the principles we have outlined that would enable us to suspend the current action.‎”

The row over guards is now focused on SWR, which normally serves about 600,000 trips each day on a network encompassing London and counties including Surrey and Hampshire. RMT strikes on West Midlands Trains were suspended last week.