The scheme will allow people free bus travel after the morning rush hour
Free off-peak bus travel for over-60s and disabled travellers is being extended so they can travel anywhere in England using a single pass.
Up to 11m people will benefit from the new National Travel Pass smart cards. But an MPs' report has warned many buses may not be equipped to read them.
Some councils, with areas popular among tourists and shoppers, fear the annual £1bn of government money is not enough.
The Department for Transport said it was a "fundamentally important scheme".
Transport Minister Rosie Winterton said: "For many older or disabled people the bus can be a lifeline - providing access to employment, healthcare and other essential services, as well as allowing them to visit family and friends.
"That is why we have been working hard to deliver an increasingly better deal."
Members of the House of Commons transport committee said the fact that many buses were not equipped to handle smart cards was "daft".
Committee chairman Gwyneth Dunwoody said the ability to travel freely across the country was a "great boon" but it was important to get value for money.
"The government needs a clearer strategy to move forward with integrated ticketing," she said.
Liberal Democrat transport spokesman Norman Baker said the government's funding of local authorities was so tight that councils were cutting back bus services to pay for the scheme.
"Some elderly people are losing their reduced travel before 9.30am, and carers are losing their discounts," he said.
The Local Government Association (LGA) said about 30 councils were predicting funding shortfalls of up to £2m, including Nottingham, Brighton and Hove, Harrogate and Scarborough.
ON THE BUSES
Scotland: Over-60s get free travel on buses and some coaches any time of day, including morning rush hour
Wales: Over-60s get free travel on buses any time of day
Northern Ireland: Over-65s get free travel on buses and trains, and can travel over the border into the Republic of Ireland using the same pass
This has prompted the LGA, representing more than 380 councils in England, to call on the Treasury to review its calculations for how much money will be given to individual councils to pay for the scheme.
The fare is to be paid for by the council in the area where the passenger begins their journey.
There are also concerns that in some areas the passes may not have been printed in time for the launch of the scheme on Tuesday.
Age Concern wants the passes to cater for over-60s who do not live near a bus route, or who are physically unable to use buses or trains.
A spokesman said: "Tokens for other transport, such as taxis, should be offered as an alternative.
"This would help older people living in areas without buses and those with health problems for whom bus travel isn't suitable."
Wales, Scotland and Northern Ireland already offer free travel schemes, but until now bus passes in England have only been valid for people who live in the local area.
The Department for Transport said each nation will run its own scheme, meaning a Welsh pensioner could not use their pass to travel over the border into England, or vice versa.
A department spokesman said there was potential to join up the schemes in the future, and it would work with Wales and Scotland to reach an agreement.
He added: "We believe this is a fundamentally important scheme that will help elderly and disabled people to travel more freely, such as visiting friends or family who live outside their local areas.
"Due in part to cost implications, there are currently no plans to extend concessionary bus travel into peak times or on to other modes of transport.
"Local authorities still have the option, at their own expense, to extend the scheme for their residents. This is right because they know about local needs and circumstances."