The thing is there are multiple companies/sectors involved here, and this isn't addressing the worst of them (yet, if ever).

First you have the railway lines themselves. These are run by Network Rail, which is already a part of the Department for Transport. This part covers a significant expense, but it's needed and run fairly lean.

Then you have the train companies. These are the ones running the trains, they are typically private businesses. They lease rail stock (trains and carriages) and sell tickets, while paying Network Rail for the use of the lines. These are the customer facing businesses, and South Western Rail is one of them and the one nationalised in this story. In spite of having high ticket prices and revenue, they have low profits due to high costs.

Lastly you have the rail stock companies. These are the real villains, frankly, much moreso than train companies. They set leasing prices for trains, and in turn cause the train companies to run at paper thin margins. They aren't customer facing, so the public eye isn't upon them and they get away with a lot. They have established long term contracts, so simply nationalising a train company won't end this deal.

However, nationalising train companies does mean that the government (either the DfT or the new Great British Railways) will be negotiating with rail stock companies. In theory, the government are a bigger entity, so have a better negotiating position, and also they should be more motivated to bring the costs down. Private rail companies make more money overall with paper thin margins on high prices, not only because a small percentage of a bigger number can be bigger, but because having a small margin puts them in a better negotiating position with local government ("You have to give us a good deal, we can't afford to operate otherwise, and you need us").

So nationalising train companies might lead to lower prices in future, through fairer leasing rates on rail stock. However this won't start to happen until these contracts are renewed.

Really, a much heavier hand is needed from the government, one that focuses specifically on the rail stock leasing sector.

Awesome, now get rid of first bus parasite monopolies.

Renationalaizing and extending rail would solve so much in basically every country in Europe. There is soo much demand for it and rail companies everywhere are just cranking up prices without expanding at all.