Scarborough Council received a grant of £839,000 towards the scheme, which is estimated to cost more than £1.82m – leaving a shortfall of around £980.000.

The scheme allows anyone aged 60 and over to travel free on buses anywhere in England and has proved costly for towns such as Whitby and Scarborough, which are popular with holidaymakers.

Mr Goodwill said: “The frustrating thing is that although the total amount of money allocated has been about right, the way it has been allocated to local authorities is completely wrong.

“This has resulted in some councils making a big profit while others, especially popular destinations, have lost out big time.”

The MP raised the issue in the House of Commons last month during his first full debate as transport shadow minister.

He said during the debate that the use of the concessionary fares had increased by more than 30% since April and there had been a significant increase in bus passengers.

He added this has resulted in an increase in costs for some local authorities, particularly hotspot destinations such as coastal towns and urban centres, where the share of the extra money provided by the Government this year has fallen short of demand.

People from places as far and wide as Middlesbrough and Guisborough can board direct services to Whitby and Scarborough and take advantage of the scheme.

Mr Goodwill said: “The borough of Scarborough is becoming a victim of its own success as an attractive place for visitors to come because the Government has underestimated demand by a major amount.

“I am all in favour of the scheme but I don’t agree with the Government taking credit for it when half is having to be paid for by local council taxpayers.”

This year’s budget was set at £3.3 m to deal with the new national scheme that came into operation in April, compared with £1.5m when senior citizens with passes were restricted to their local area.