A Virgin spokesman said the company had increased the number of staff handling compensation by 80 per cent to process the payments.She said: “We apologise for the current wait that customers are experiencing when claiming delay repay. Due mostly to problems with the infrastructure that are outside of our control, there have been 70 per cent more claims than anticipated.”Who runs Britain’s trains and rail network?Britain’s railway network is run by Network Rail, a 100 per cent public-owned body after its predecessor Railtrack was nationalised in 1996.Its main “customers” are the privately owned train-operating companies that carry tens of millions of passengers around the UK ever year.Network Rail owns the infrastructure, including 20,000 miles of track, 40,000 bridges and tunnels and 2,500 stations.What is the problem?Network Rail is spending billions modernising the network and sometimes these works can over-run, which means that lines have to remain closed during busy periods.Commuters are infuriated by the delays and blame the train companies, which in turn blame Network Rail and have to seek compensation for any delays.What does the Government want to do?Chris Grayling, the transport secretary, is keen to introduce a “vertical model” on some lines which would allow train companies to have a say over the maintenance of the track.This could mean train operators being given a say over running sections of the network as new franchises are awarded by Mr Grayling, starting as soon as next year.Will it make a difference?Mr Grayling hopes so. When he was shadow transport secretary, he said that the “complete separation of track and train into separate businesses” was “not right for our railways”.The changes could eventually lead to cheaper fares and a more reliable train service for millions of commuters because Mr Grayling also blamed this separation of the train from the track for pushing up “the cost of running the railways – and hence fares – and has slowed decisions about capacity improvements”. Mr Grayling is due to set out the proposals in a speech at Conservative think-tank Policy Exchange on Tuesday.The plans will alter key elements of the privatisation of British Rail by John Major’s Conservative government in the Nineties by giving train companies control over the tracks again.It will be a shot across the bows of Labour leader Jeremy Corbyn, who has used a threat to renationalise the railways to win over the support of frustrated rail commuters in middle England.Mr Grayling spoke of his desire to give train operators control over the track when he was Tory front-bench transport spokesman a decade ago. The rail network’s structure dates from 1996 when John Major’s government sold off British Rail and put a new private company, Railtrack, in charge of the rail network.However, Railtrack collapsed in 2001, prompting a major political row when Stephen Byers, then the Labour transport secretary, said its private shareholders would not be compensated.Network Rail, which is 100 per cent owned by the taxpayer, was set up by the government to replace Railtrack with a £300 million of public money.Train operators have to rely on Network Rail for carrying out repairs.Network Rail also decides the duration of maintenance and when works will take place.Earlier this week, it emerged that Network Rail was responsible for more than half the delays on Scotland’s trains over the past year. He said he wanted Network Rail to be “a public-sector body that acts like a private business, with a clear focus on what customers want”.This week, Network Rail also warned of major works at busy London stations which could mean that the festive getaway is a misery for millions of people.Liverpool Street and London Bridge stations will be badly affected for most of the holiday period and many services will not run in and out of other mainline stations.Other modernisation work in the South Wales area will affect mainline services between Newport, Cardiff Central and Bridgend over the Christmas period.Ministers announced this week that more than 84,000 passengers on Southern Rail are to receive £15 million in compensation for disruption this year caused by strikes, “Network Rail track failures” and “engineering works”. The Telegraph can also disclose that Virgin Rail compensation payouts to East Coast Main Line passengers have been delayed because of a 70 per cent jump in claims.Virgin admitted that nearly 25,000 travellers have been waiting for months for compensation for delays caused by Network Rail in September. Network Rail will be stripped of its control over Britain’s train tracks and power will be handed to operators in the biggest shake-up of the railways for decades, the Government is to announce.In an attempt to end delays and reduce fares, Chris Grayling, the Transport Secretary, will say he wants the publicly-owned Network Rail to share responsibility for running the tracks with private train operators.It means that rail companies such as Virgin and Southern would become responsible for repairs and maintenance for the first time, ending Network Rail’s monopoly.The Government hopes the change will incentivise train companies to complete repairs more quickly and possibly herald cheaper fares. The news comes as passengers prepare for more upheaval over Christmas, with passengers being told by Network Rail that they face a “crescendo” of maintenance work over the festive season.It was announced yesterday that rail fares will go up by an average of 2.3 per cent – more than twice the rate of inflation – from Jan 2. Chris Grayling is due to unveil the proposal in a speech at the Policy Exchange on TuesdayCredit:Julian Andrews Mr Grayling is understood to want to challenge Network Rail’s monopoly on repairing and upgrading tracks and signalling. One idea is to introduce “vertical integration” which would mean train companies having power over the running of their sections of the rail network when franchises are awarded. Mr Grayling and the Department for Transport declined to comment.Earlier this week, Mark Carne, the chief executive of Network Rail, unveiled plans to “put the passenger at the core of everything we do” to deliver a more “reliable” railway.Mr Carne announced the creation of boards – with passenger representatives – to oversee the running of parts of the railway. Britain’s rail network is currently run by Network Rail We think, with hindsight, that the complete separation of track and train into separate businesses at the time of privatisation was not right for our railwaysMr Grayling The rail network’s structure dates from 1996 Credit:Dan Kitwood/Getty Images Want the best of The Telegraph direct to your email and WhatsApp? Sign up to our free twice-daily Front Page newsletter and new audio briefings. He said then: “We think, with hindsight, that the complete separation of track and train into separate businesses at the time of privatisation was not right for our railways. “The separation has helped push up the cost of running the railways – and hence fares – and has slowed decisions about capacity improvements. “Too many people and organisations are now involved in getting things done – so nothing happens.”In publicity material sent out ahead of the speech, Policy Exchange said Mr Grayling’s vision will “put the passenger at its heart, ensuring that journeys are safe, quick, and provide value for money”.Currently, Britain’s rail network – which is run by Network Rail – and the trains that travel on it are run by completely separate companies.