Rail minister Claire Perry has dashed hopes her department will provide the cash for a crucial study holding up more twice hourly train services between King's Lynn and Cambridge and Norwich and Cambridge.

She said after meeting MPs 'we can't write a cheque' or 'turn on a tap' after a plea to contribute to an estimated £5m piece of work at Ely North Junction.

Last year the £35m upgrade to the junction – which was set to start in 2016 – was put back to at least 2019, when the next funding period starts. Network Rail says a study needed to be conducted into the scheme.

But Ms Perry said she would provide 'support' and they would look at whether Network Rail's estimate was realistic and if the costs could be lowered. She also said other sources of funding could be found from the local enterprise partnerships (Leps).

'We are very keen to do this, but we know there isn't any money to do it,' she added.

It comes just days after MPs, local leaders and rail bosses met in Ely to put pressure on Network Rail to bring its plans forward and South-West Norfolk MP Elizabeth Truss said they would be putting the case for a contribution towards the £5m cost of a feasibility study from the Department for Transport.

Ms Truss said after yesterday's meeting: 'It was a very constructive meting. What she said is there isn't currently money in the budget in control period five [the funding scheme from 2014 to 2019] for a feasibility study, but as we discussed at our meeting on Friday, there are partners including the Leps and councils who are potentially willing to put their hands in their pockets. 'What they need to know is what they are putting their hands in their pocket for. What we discussed today is a realistic cost because that £5m may not actually be the cost of the feasibility study.' 'A number of bodies have said they will look at funding this. What we need is a concrete plan because the problem before with the proposal was it didn't deal with the issue of crossings at Queen Adelaide. They DFt has said they are committed to working with us on it. We are going to keep the pressure on to make sure this things happens.'

New Anglia chief executive Chris Starkie said: 'The key thing from our perspective is we could wave a chequebook at it, but what we wanted was the minister to give us a reassurance that Network Rail participates and takes that piece of work seriously and if we collectively fund it locally, that Network Rail will carry out the work that is required.'

He said they want to fund the study so the work was ready to be done at the beginning of the 2019 five year funding period rather than at the end of the five year programme of work.

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