Rail passengers should not be allowed to board long-distance trains without a reservation, according to Virgin Group.
The firm, which jointly operates trains on the West Coast Main Line (WCML) under the Virgin Trains brand, said inter-city services should use the Eurostar model of requiring customers to book a ticket and a seat for a particular train.
Operators are currently often obliged to accept walk-up fares, meaning they have no control over the number of people getting on a particular train unless it is deemed unsafe.
They are also obliged to stick to rigid timetables which results in them running trains even when demand is low.
In its submission to the Government-commissioned Rail Review, Virgin Group said this leads to some trains so packed that passengers are forced to stand for several hours, while others are mostly empty.
It called for ticketing to be simplified by introducing dynamic pricing, which would lead to higher prices for popular trains and lower prices for less popular trains.
Virgin Group also wants the franchising system for long-distance routes to be replaced with an auction for train slots, in a similar way to how airlines secure the right to operate flights from airports.
It gave the example of London to New York flights being offered by numerous airlines, and said multiple rail firms could operate major routes such as London Euston to Manchester.
Competition between operators would prevent passengers being squeezed in a drive for profit as they would have the option to switch to a rival company if standards dropped, Virgin Group's submission stated.
It claimed that selling the slots without an expiry date would give companies more chance to respond to economic turbulence, whereas the franchise model means there are only a few years to recoup any losses.
An auction would generate a "significant one-off boost in tax receipts" while operators would also commit to a certain percentage of their profits from each slot going to taxpayers, Virgin Group added.
Mick Cash, general secretary of the Rail, Maritime and Transport union, said: "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.
"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 are actually proposing a version of the broken rail franchising model pumped on steroids when what is really needed is an end to this nonsense and public ownership of our railways."
The Rail Review is being chaired by former British Airways chief executive Keith Williams, and his inquiry will conclude in the autumn.
Virgin Group's submission was written before the recent decision by the Department for Transport (DfT) to disqualify Virgin Trains' bid to continue operating West Coast Main Line services due to a row over pensions.
Its recommendations are "more pertinent than ever given this news", according to Patrick McCall, a senior partner at Virgin Group.
He went on: "Keith Williams has said that franchising cannot continue as it is now, and it is clear we need systemic industry reform which is driven by principles and a whole-system redesign.
"Indeed, it is highly questionable whether any franchises can be let sensibly, or robustly, as things stand.
"This will not be an easy fix. Every option will have downsides and there will be some difficult decisions to be made.
"But there should be no dogmatic fixation on models or ownership. Instead, we must develop a system which optimises the benefits for passengers, taxpayers and communities and which enables train companies to evolve as the world evolves around them. We must be both visionary and pragmatic."
Virgin Trains - a joint partnership between Virgin Group and Stagecoach - has run WCML services since 1997.
The winning bidder for the new West Coast Partnership franchise - due to be awarded in June - will be responsible for services on both the WCML from March 2020, and designing and running the initial HS2 high-speed services from 2026.
A joint bid was entered by Virgin Group, Stagecoach and SNCF, but this was one of three Stagecoach bids ruled out earlier this month because they did not meet pensions rules.
Virgin Group boss Sir Richard Branson said at the time that he was "baffled" as to why the DfT did not discuss the issue before making its decision.
But the department insisted it has "total confidence" in its process.