Not necessarily, as the UK would still have to comply with EU regulations about the separation of track and train operations. This has been enshrined into British law. While Brexit will free the UK from such regulations, there is still a legal process to follow as the law would have to be changed to allow for a vertically integrated company to be created (like the old British Rail). Private operators (FOCs and open access passenger operators) are likely to see a reintegration effort as unfavourable as it would hurt their business. They will try to prevent this from happening through lobbying, legal proceedings and judicial reviews of proposed changes.
A second option would be to renationalise operations, but keeping them separate from the infrastructure. Problems caused by fragmentation are unlikely to go away, as there would still be two companies involved which have their own targets.
The problems caused by the franchising process might go away, only to be replaced by different problems. With DfT wanting to control everything on the railways (up to the kind of seats being put in the trains) and the Treasury wanting a maximum return on investment, would things really get any better if the operations are now controlled directly by the Government? At least the private TOCs can try to push back against some DfT enforced decisions as they realise it could be ill-received by their customers, thus harming their business...
It's not true that there must be separate infrastructure and operations companies under EU law, merely that there is separate accounting for the two aspects of the business.
That's how DB and SNCF and the rest continue to operate as single bodies (though they do have separate divisions which are largely independent of each other).
But privately-owned freight and open access is separate from the DfT franchising system, so whatever happens to the franchises there will still need to be a level playing field for operators (TOC access agreements etc).
Also Heathrow Express and HS1 (with HS2 to come) are not part of the Network Rail asset base or its regulation. Eurostar is another separate body (in largely French ownership).
Most new rolling stock is now maintained by the manufacturer, not by the TOCs, with long-term contracts in place.
DfT is also not in total control of "the railway".
Scotland has its own passenger system and funding, and Wales is close to getting a devolved passenger rail operation as well.
Then there is TfL with its major share of railway concessions (LO and Crossrail), and Merseytravel which controls Merseyrail's concession.
So it's very unlikely "renationalisation" would look anything like a single integrated BR, with all these competing interests.
And BR itself, in its final decade, was essentially 4 different operations (Inter-City, Network South East, Regional Railways and Freight).
