Network Rail bosses' proposed package of six-figure bonuses have been condemned and branded "unacceptable" by transport secretary Justine Greening.

Chief executive Sir David Higgins could get a £340,000 payout under the bonus scheme to be considered by the firm's members this month.

Greening urged the company to be "responsible" and "exercise restraint".

The potential bonuses come amid anxiety at Westminster about executive pay and after Network Rail this week admitted health and safety breaches over the deaths of two teenagers killed at a level crossing.

Olivia Bazlinton, 14, and Charlotte Thompson, 13, were hit by a train in 2005 as they crossed the tracks at Elsenham station footpath crossing in Essex.

The firm also faces prosecution over the 2007 Grayrigg train crash in Cumbria in which one passenger died.

The proposed bonus scheme would see Network Rail directors receive annual bonuses of 60% of their annual salaries.

They include Sir David, whose salary is £560,000, group finance director Patrick Butcher (£350,000), operations director Robin Gisby (£330,000), director of asset management Peter Henderson (£440,000), investment projects director Simon Kirby (£330,000), and planning and development director Paul Plummer (£310,000).

Labour's shadow transport secretary Maria Eagle said Downing Street had admitted Greening could not control bonuses.

"The prime minister has now passed the buck to Justine Greening on Network Rail bonuses while admitting that she does have the power to act over the outrageous bonus scheme being proposed by the taxpayer funded company, despite her attempts to imply otherwise.

“Network Rail’s Articles of Association are crystal clear. Thanks to the Department for Transport’s role as a ‘Special Member’ of Network Rail the transport secretary could have attended, or appointed a representative to attend, meetings of the company’s Remuneration Committee and voted against these proposals. It is not too late for her to do so at next week’s General Meeting of Network Rail.

“The Transport Secretary should stop spinning, recognise that times have changed and use the power she clearly has to ensure that this bonus scheme is not agreed at a time when fares are rocketing and performance on the railways is deteriorating.”

Greening said: "This proposed package is unacceptable. Network Rail needs to be responsible and exercise restraint."

The transport secretary blamed Labour for a system in which ministers "have no powers to block Network Rail executive pay and which in 2008 saw bonuses of over half a million given out to the chief executive even when there were serious failures".

"This is clearly a flawed system which we have already addressed as part of our forthcoming Rail Review which will make Network Rail more accountable," she said.

David Cameron's official spokesman said reports of the size of Sir David's proposed bonus were "speculative", but added: "The prime minister has been very clear about his views on pay and bonuses and he has consistently said he wants to see responsibility and restraint."

Former Labour rail minister Tom Harris has tabled a motion, signed by 27 other MPs from his party, calling on Sir David and the firm's directors to turn down any bonus payment.