Rail union boss Mick Lynch has warned his members will not hesitate to take further strike action as he said the disruptive dispute had "a long way to go yet".
But he insisted the Rail, Maritime and Transport (RMT) union would engage in a "constructive dialogue" and work with Network Rail and the train firms to reach a settlement that is agreeable to both sides.
Mr Lynch was speaking to Sky News as train services were hit by the third walkout this week over jobs, pay and conditions.
Only a fifth of services are running and half of the lines are closed.
Passengers have been warned by rail operators that they should only travel by train if necessary and to check their journey in advance.
Signalling little sign of a breakthrough in the current industrial strife, the RMT general secretary said: "There's a long way to go yet.
"Most of the stuff our members voted very heavily in favour for action about are what's on the table now and they have not diluted very much the stuff they want and that's true of the train operators and Network Rail."
He added: "We have got to be very cautious about what they call progress.
"There may be progress in their agenda, but it doesn't mean that our members are going to accept those changes just because the company wants them.
"We have got to work that problem through with them.
"We will do that in a constructive dialogue but there's still a long way to go on this dispute."
Mr Lynch went on: "The whole point of a dialogue and a negotiation is that people change their position and you get to a new position that doesn't belong to either party so that you can form a constructive way forward.
"At the moment the companies are giving us all the reforms they want but they aren't listening fully to what we need and our members need to get a decent working life on the railway.
"They need to change their position in terms of what they are offering in terms of pay, what they can do for job security and the way that they engage their staff and come to agreement with us about the way people work.
"We will work with them on that. We have not named dates. We will review where we are in discussions next week and then we will decide if we need to take more action.
"Network Rail issued a notice a formal letter of redundancy last week, that's entirely unacceptable as a step to take in the middle of a negotiation."
Meanwhile, Boris Johnson told Sky News the public has a right to expect reforms to rail services.
He said: "I would say, given the circumstances we're in, I think what we want to see is reform and improvement in the way the railways work, and modernisation.
"When you've got a 25% fall in ridership, which we've got at the moment, we've got the government putting billions and billions (into it).
"We're putting more into the railways than any previous government.
"I think the travelling public has a right to expect some basic reforms, like with ticket offices, like with walking time, and some of these other practices that really nobody defends except the union leaders."
Many people were able to avoid the rail disruption during the first two days of the strikes - Tuesday and Thursday - by working from home.
But for those with long-standing plans to travel by train for weekend events, this was not an option.
Popular seaside resorts - such as Bournemouth, Blackpool, Margate, Llandudno, and Skegness - will have no rail services.
And even the services that are running will only operate between 7.30am and 6.30pm, with several major stations such as Birmingham New Street, Liverpool Lime Street and Manchester Piccadilly closing at 7pm.
Disruption is expected to affect many Sunday services too.
Passengers with pre-booked tickets for Saturday are able to travel on Friday, Sunday or Monday instead, or claim a refund.
This week's strikes are estimated to have cost the rail industry up to £150m in lost revenue and aborted planned upgrade work.
Talks between the RMT and rail employers have been held throughout this week and are expected to resume in the next few days.