The firm argues seats should be sold as reservation-only, as part of a broader break-up of the rail franchise system.

The firm, which operates trains on the West Coast Main Line, said customers should have to book a ticket and a seat for a particular train.

Its proposal is part of Virgin's submission to a government-commissioned review into the rail system.

Currently, train operators typically accept walk-up fares, meaning they have no control over the number of people getting on a particular train unless it is judged unsafe.

They are also obliged to stick to rigid timetables which Virgin Group said leads to some trains so packed that passengers are forced to stand for several hours, while others are mostly empty.

Under its plans, Virgin would also discard peak and off-peak pricing tiers.

The train operator has also proposed a break-up of the franchise system, where firms bid for contracts which run for a number of years.

Instead, Virgin says that bundled slots on services should be owned "in perpetuity" by train operators to allow operators to act like "normal" businesses, with more freedom to set different ticket prices across services.

Virgin described the current system as "something of a straight-jacket" for operators.

It said the process of bundling slots would work in a similar way to how some football broadcasting rights are auctioned.

Virgin argues that the move would encourage investment and allow operators to "innovate and adapt to a changing market".

'Total chaos'

But unions said the plans would lead to "total chaos".

"What Virgin are proposing is a de-regulated free for all where private train operators slug it out on the most lucrative routes on a slot-by-slot basis," said Mick Cash, general secretary of the Rail, Maritime and Transport union.

"It would lead to total chaos with passengers trapped in a transport nightmare of escalating fares where prices rise by the minute according to availability.

Virgin's submission was written before the recent Government decision to disqualify its bid for the West Coast Partnership. In response, Virgin has said it may close down its train business altogether.

Should Virgin's suggestions be brought in, the firm may be considered to be in an advantageous position, with existing experience of operating flights through its Virgin Airways business.

The William's Review, described as a "root and branch" review of the UK train industry, is being led by Keith Williams, the former chief executive of British Airways,

Mr Williams has previously refused to rule out any options, including bringing the rail industry into public ownership.