In the small hours of Friday morning, a former member of the shadow cabinet, well known as an opponent of Jeremy Corbyn and usually unafraid to deliver criticisms of his leadership into any microphone on offer, was invited on to the Today programme to respond to Labour’s dismal, wooden spoon performance in the Sleaford byelection. Much as he was tempted by the invitation, he turned down a slot in prime time.

He was far from the only Labour MP to decline the chance to articulate despair about the party’s prospects. The interesting thing about the two months since the Labour conference is not how many of its MPs are to be heard talking about their party’s plight, but how few currently want to voice an opinion in public. Where once every reverse saw the airwaves crackle with Labour MPs attacking the leadership, now there is largely silence.

This needs some explaining. Is it because Labour’s position has so improved that the parliamentary party no longer feels that criticism is warranted? No, it is hardly that. The party’s poll ratings remain dire. If anything, they are getting worse. The latest poll from You Gov gives a 42%-25% lead to the Conservatives over Labour. This pollster suggests that barely more than half of the people who supported Labour at the last election (which it lost) would support the party at an election tomorrow. Other polling organisations tell a similarly bleak story. Translated into parliamentary seats at an election, these numbers suggest a crushing Tory landslide and a devastating Labour defeat.

Our most recent Opinium poll had equally terrible findings for Labour when two key drivers of voter behaviour were tested. On the economy, just 18% of voters thought Labour was the best bet against 44% preferring to trust the Tories with the national finances. Forty-five per cent said Mrs May was the better choice for prime minister; just 17% favoured Mr Corbyn in Number 10. So if satisfaction with the party’s current prospects can’t be the reason for the curious silence of Labour MPs, can it be explained by a belief among them that things are going to get better? No, it is not that either. Jeremy Corbyn’s reputation with his MPs has not improved since more than 80% of them declared that they had no confidence in the leader back in June. Their agonies have only been increased by the aftermath of the Brexit referendum. There is a vast chasm between pro-Remain supporters in metropolitan areas and pro-Brexit folk in Labour’s traditional heartlands in northern England, the Midlands and Wales. Worse, there is little sign of any consensus about how to resolve this existential dilemma for the party. “Our position is cataclysmically depressing, obviously,” says one Labour MP, in a matter-of-fact sort of way. Another Labour MP, not a person normally given to defeatism, forecasts, “I really do believe it will be the end of the party” if something does not happen to improve their prospects before the next election.

Sheer resignation comes into the explanation for the silence of Labour MPs. When Mr Corbyn was re-elected as leader in the summer, and by a handsome margin, it confounded the idea that he could be quickly removed through the mechanism of a challenge launched by the parliamentary party. Talk of repeated bids to unseat him – the so-called “attrition strategy”– has evaporated.

In the case of a lot of Labour MPs, the silence is more than a product of despair. It is a conscious choice, a considered decision to pursue what I am going to describe as a Shut Up Strategy. Owen Smith’s failed leadership challenge taught them some valuable lessons. One was about themselves and how they looked to many of Labour’s members and registered supporters. One former shadow cabinet member explains: “The PLP – capital letters – is a swear word. Among many members, it means careerist, failure, disloyal.” In his first year as leader, Mr Corbyn was repeatedly attacked by his MPs. Even when the criticisms were richly merited, the overall effect of the hostility of his parliamentary party was to sanctify him in the eyes of activists who saw him not as the source of their party’s tribulations, but the victim of them. It helped him enormously that the leadership challenge was framed as a “coup”; that it was seen as a struggle that pitched MPs against members, Westminster versus the grassroots.

Labour parliamentarians are now keeping stumm so they can’t be blamed for dividing the party and culpability for its unpopularity will be landed on the leadership. Says one: “The ownership of failure has to be hung around the necks of Corbyn and (John) McDonnell.” Allied with this is a recognition that it is not sufficient for the centre-left to keep saying that Corbynism is an electorally suicidal dead end. The moderate left needs to look to its own failings and respond with a lot of intellectual reinvention and policy renewal.

This silence in the national media should not be confused with inactivity. Their constituencies have become the prime focus of the energies of many Labour MPs. If the first chapter of the battle for the soul of the party was played out on the Westminster stage, the next one is being waged at a local level. Around 300,000 new members have joined Labour during the Corbyn era. The result has been a dramatic transformation of many local Labour parties, especially in metropolitan areas. There are Labour constituency parties that have quadrupled in size over the past 18 months. This influx has brought with it the menace of deselection in areas where Momentum, the leftwing group set up to back Jeremy Corbyn, has been recruiting heavily. A wave of attempts to unseat Labour MPs has been widely expected.

As it turns out, the centre-left is doing much better in these local struggles than many anticipated at the time of Mr Corbyn’s re-election. They remain under siege in Merseyside, where the militant left has been historically strong, but the moderates are doing remarkably well elsewhere.

At the height of the viciousness over the leadership during the summer, the party was forced to take the extraordinary step of suspending all local party meetings. Since that suspension was lifted, many constituencies have been conducting their annual general meetings. Boring name; significant purpose. The most important thing that the AGM does is to elect key local officers: the chair, the secretary and the treasurer. The chair controls the agenda of meetings. The secretary and the treasurer have access to membership lists. Who wins these roles is a good litmus test of the state of play within Labour because these posts are the first line of defence against deselection.

In the London constituency of Walthamstow, Stella Creasy had been under severe pressure from Momentum activists, but at the recent AGM the tide was turned. All the officer positions were secured by moderates. They have also prevailed at recent AGMs in Bermondsey, Camberwell, Dulwich and Lewisham.

This is especially significant because south-east London is an area of historic strength for the hard left where Momentum has been extremely active. There was a potently symbolic outcome in Chesterfield, once represented in parliament by Tony Benn, the spiritual godfather of Corbynism. There, the moderates made a clean sweep. These victories have drawn a rare compliment from the Trotskyists at the Socialist Worker where it was recently lamented: “The left’s defeats show that the right has stronger organisation inside Labour.”

As the old leftists liked to say, the struggle takes many forms

There was another boost for the centre-left at last month’s conference of the London Labour party, when the election for the position of vice-chair saw the moderate candidate win 85% of the constituency votes. Some of this is the result of well-organised Labour MPs waking up and mobilising the party’s more mainstream supporters. Shrewd MPs have also made a serious effort to connect with their new members by running “training sessions”.

“I’m doing a hell of a lot of work with local party members to make sure there’s no issue with me,” says one MP from the north-west. “I am taking my new members out knocking on doors and taking them to places where I know they will hear some home truths from voters.”

Momentum has made tactical errors. In some constituencies, hard left activists have gone after Labour councillors. Realising that they were more vulnerable to deselection than MPs, these councillors are fighting back. Momentum has a massive data base, but that has proved a less powerful weapon for rallying members against Labour MPs than many originally anticipated. The so-called “clicktivists” appear to behave as their name suggests they might behave: they aren’t terribly keen to turn up for meetings, and it is at meetings that these local power struggles are being played out.

It is a further encouragement to Labour MPs that Momentum is now descending into a poisonous internal faction fight between rival flavours of far leftists.

Do not mistake the sound of silence in the national media for an absence of battle. The war for Labour’s soul goes on. As the old leftists liked to say, the struggle takes many forms. The one that counts at the moment is at the grassroots. Rather against expectations, the moderates are prevailing.