The simple answer here is that the answer is complex.
With regards to the simple question of whether the current franchising structure should end (as soon as franchise agreements become void) the answer is a simple yes. Privatisation and marketisation are two very different things and the current franchising system is a state sponsored racket.
With regards to whether the railways should then be run as British Rail was, the answer is very much no.
The system i would put in its place is one which essentially separates the profit making lines and those which already require subsidy. For the network as a whole those routes which are currently in receipt of subsidy or which only have an hourly service (where no competition is obviously taking place) should be ran by the state at their current level with ticket prices continuing to rise by inflation each year to maintain the current subsidy level.
For those routes which are profitable and have multiple services i would essentially have the state remain operator of last resort with stock held should the capacity be needed but essentially free the private sector to compete in an open access model. Essentially if Virgin and First both wish to provide services on the East Coast main line we would let them, Open access operators would be charged for access serving whatever stations they wish on an annual basis (if First thinks there is more money to be made by dropping or adding stations or going via a different set of track they should be able to - Grand Central for example wanted to run a Huddersfield-London service but going via Birmingham). They would simply register for access on x route per year (paying the appropriate charge per mile and station stopping fees) and then meet requirements designed to improve service such as only operating stock less than 30 years old which they must purchase themselves (right now the state does it because it gets transferred with the franchise) and meeting the environmental regulation ect. Firms would be able to compete on routes, on stock (as a tall guy i would set off an extra 15 minutes early to catch the service ran with more leg room) and on price much more freely.
On the infrastructure side things are more complex. Firstly Network Rail despite being inefficient compared to European counterparts is already state owned and should remain so (privatising that aspect only works if the state stops dictating which railway lines it wants building and abolishes planning law to the point that firms can like the Victorian Age build their own) but there is a question of to what degree the state should subsidise Network Rail directly. Right now for example Network Rail piles up long dated debt instead of receiving as much direct subsidy from government as it otherwise would. There is an argument that you should raise fares to compensate, cut the loss making parts of the network to remove the cost of maintaining those sections or simply put the debt onto the government books and directly increase the amount of taxpayer funding. Personally i am not a massive fan of piling up what amounts debt guaranteed by the taxpayer and would rather the money currently thrown away via foreign aid was redistributed to the railways and other infrastructure. I would also probably take all rail stations into public ownership, especially since any estate development may be able to offset some of Network Rails costs.
https://orr.gov.uk/__data/assets/pdf_file/0013/40351/uk-rail-industry-financial-information-2017-18.pdfPage 16 of this report nicely illustrates which franchises are loss making and which are profitable. Essentially the problem is with Scottish Rail, Welsh Rail, MerseyRail, Northern and the West Midlands.
In this context it may be more prudent to transfer responsibility for operating at least some of those routes to regional bodies. Merseyside, Greater Manchester, West Yorkshire and South Yorkshire (not sure who runs in Nottinghamshire) have the bulk of those running through them. So either creating a single body or separating per county would allow more local control of the routes with a stipulation that subsidy from central government will be removed (so they'll either have to select which routes are actually important, create new ones or raise taxes locally).