The operators of the troubled Thameslink train line may be stripped of their franchise should a revised, emergency timetable fail to stem cancellations, according to a government source.

Govia Thameslink Railway, which has been backed by the Department for Transport over years of severe disruption on Southern through staff shortages and strikes, could be given notice within weeks, after the chaos resulting from the timetable change in May.

GTR will introduce a redrawn timetable from 15 July to tackle disruption which so far shows little sign of abating, with about 20,000 trains cancelled or severely delayed in the last six weeks.

A government source told the Guardian that if the service continued to be chaotic it would be the final straw for GTR. “If that goes wrong, that will be the final straw for them. That surely has to be enough.”

However, an ongoing review by Whitehall officials would also need to show GTR had breached its contract for action to be taken. The DfT review may not be concluded before parliament goes into recess, which could defer any decision.

Preparations for any operator of last resort to step in, as on East Coast after Stagecoach defaulted on its franchise, would also mean a transition of several months.

The transport secretary, Chris Grayling, and the rail minister, Jo Johnson, held separate meetings with GTR executives and MPs last week to discuss concerns. Although reliability on Northern trains has improved since a decision to cancel 6% of services in advance at the beginning of June, Thameslink trains have remained chaotic.

Enhanced compensation schemes are set to be announced for Thameslink passengers, agreed by GTR weeks ago, although the detail has been kept within the DfT. Last week the government said affected Northern passengers around Lancashire, Greater Manchester and Cumbria would receive a month’s free travel for the disruption there. A similar deal is expected for parts of the GTR franchise, although Southern services within the franchise have been running comparatively well since May.

A DfT spokesperson said: “GTR passengers are encountering unacceptable service levels and the transport secretary and rail minister have been clear it is their priority that this is put right as soon as possible and passengers are compensated for the disruption.

“We will investigate whether GTR have breached their contracts and we won’t hesitate to take tough action against them if they are found negligent.”

Unions dismissed government threats to finally axe GTR and suggested Grayling should examine his own position. Mick Whelan, general secretary of Aslef, the train drivers’ union, said: “GTR has – not for the first time – badly let down passengers and staff with its inept introduction of a new timetable on 20 May. But the DfT, too, was at fault for creating the GTR super-franchise in the first place. They have been working hand in glove and are both to blame.”

Labour said GTR should be permanently stripped of the franchise, and the network renationalised. Shadow transport secretary Andy McDonald said: “Passengers have needlessly suffered years of delayed, cancelled and overcrowded services because of Tory failure and their refusal to strip incompetent train companies of their franchises, and services be brought permanently back into public ownership, not just as a temporary measure.”

The RMT’s general secretary, Mick Cash, said. “Telling these basket-case companies that they are drinking in the last chance solution is empty rhetoric … Chris Grayling has personally propped up Britain’s failing rail franchises while RMT members have been deployed at the sharp end as human shields to bear the brunt of the public anger, threats and abuse.”

Although Grayling has publicly singled out GTR for criticism, and the chief executive, Charles Horton, has already resigned, the firm believes blame should be more widely shared around the rail industry – and with the DfT. Factors such as delayed electrification in the north-west, which threw Northern’s timetable into disarray, and delayed train deliveries in Scotland impacted services which interact with Thameslink’s on main lines to London.

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An independent inquiry into the timetable fiasco, carried out by the Office of Rail and Road, is expected to report in September.

A GTR spokeswoman said: “We are sorry for the disruption which the rail industry is working very hard to fix. We are re-planning how we use our trains and train crew to introduce a new interim timetable on Thameslink and Great Northern which will operate from 15 July. This prioritises peak-hours services and reduces service gaps. This is a key stage in our work to provide a more reliable service to passengers over the coming months.”