The RMT union says Transport Secretary Grant Shapps should "get in the (negotiation) room or get out the way" following a second day of walkouts this week by tens of thousands of rail staff, as a row over pay, jobs and conditions continued.
Passenger numbers plunged to less than 20% of normal usage on Thursday, with only around one in five trains operating, and half the network closed.
Major railway stations, including Edinburgh Waverley, London Euston, London Paddington and Liverpool Lime Street, were far quieter than usual, with many people opting to work from home instead.
How the day unfolded - see latest updates
Disruption is set to continue for the rest of the week, as only 60% of trains will run on Friday, and another strike is planned for Saturday.
Further talks between Railway, Maritime and Transport (RMT) union and Network Rail aimed at ending the dispute were held on Thursday but no resolution was reached.
Downing Street has called for the industrial action to be called off "as quickly as possible" and said it was a "question for the unions" whether to go ahead with Saturday's action.
But the RMT accused Mr Shapps of "wrecking" negotiations by not allowing Network Rail to withdraw their letter "threatening redundancy for 2,900 of our members".
RMT warns rail strikes could 'escalate' if deal not struck
Around 40,000 RMT members at Network Rail and 13 train operators walked out again on Thursday.
The RMT is seeking a pay rise of at least 7% for its members, while employers have offered a maximum of 3%.
Speaking after the latest day of action, Mick Lynch, the RMT's general secretary, said: "Our members are leading the way in standing up for all working people trying to get a pay rise and some job security.
"In a modern economy, workers need to be properly rewarded for their work, enjoy good conditions and have the peace of mind that their job will not be taken away from them.
"Grant Shapps needs to get in the room or get out of the way so we can negotiate with these companies who we have successfully struck dozens of deals with previously.
"What we cannot accept is thousands of railway workers being thrown on the scrapheap after being praised as heroes during COVID.
"RMT will continue its industrial campaign until a negotiated settlement is reached."
In response, Transport Secretary Grant Shapps, said: "This is a total lie from the RMT and its General Secretary. I have had absolutely nothing to do with either the issuing of a letter from Network Rail, the employer, to the RMT - or any request to withdraw it.
"I understand that the letter makes no mention of 2,900 redundancies, but I do know it confirmed Network Rail would be introducing desperately needed reforms for the industry after the union chose strike action instead of further talks.
"The RMT continues to deflect from the fact that the only people responsible for the massive public disruption this week is them.
"I want to urge Mick Lynch and his members to stop wasting time making false claims in the media and instead return to the negotiating table so an agreement can be reached."
Here's what you need to know about disruptions
British Airways workers at Heathrow vote to strike during school summer holidays
Location technology firm TomTom said the level of road congestion in London at 9am was 83%, compared with 75% at the same time last week.
But traffic levels declined or only saw a slight increase in several other cities, such as Glasgow (down from 40% to 36%), Liverpool (down from 49% to 47%), Manchester (up from 64% to 66%) and Newcastle (up from 49% to 50%).
The figures reflect the proportion of extra time needed for journeys compared with free-flow conditions.
Broadband provider Virgin Media O2 noted a 10% uptick in network usage compared to the previous day, while some photos showed trains running with very few passengers on board.
Even those travelling to the Glastonbury festival found themselves in quiet carriages, despite only a handful of trains stopping at Castle Cary.
Traffic flows on motorways and major A roads on Thursday morning were "remarkably good", according to National Highways senior network planner Frank Bird.
He said: "Two years on (from the COVID pandemic) we've learned to work in different ways, people are working from home, so it's a very different picture.
"People are still able to carry on working even though the rail dispute is ongoing."
Prime Minister Boris Johnson earlier branded the strikes a "terrible idea", saying: "This is a government that is investing more in railways than any previous government in the last 50 years."
As well as RMT staff, Aslef-affiliated drivers for Greater Anglia also walked out on Thursday in a separate dispute over pay and conditions.
Elsewhere, British Airways staff at Heathrow have voted to strike over summer, bringing further disruption to the UK's transport network.