> The competition only existed briefly during the initial bidding process which the gov decided on.
The contracts were periodically retendered (it varied, but typically every 5-10 years). The problem is the competitive process had its own problems because it encourage the bidding companies to be overly optimistic. The East-Coast franchise infamously failed multiple times because the companies kept missing passenger forecasts and going bust.
However the competitive element was only ever for the government (in terms of how much surplus/subsidy would be required to/from the operating company over the contract). Having the branding, pricing (where not a regulated fare) etc. managed by those companies meant that they were at odds with passenger interests a lot of time.
Really privatisation was done from the wrong angle. If passengers don't get a choice in service provider then the concessions model (government pays private operators to run the service) would have made more sense. It would have allowed the government to still gain from competition and outsource management, while taking control of the more important elements. The concessions model has worked reasonably well for transport services in London (Elizabeth Line, DLR, Overground and Buses IIRC)
Also as a side point, originally the tracks and stations (or rather the management of them) was privatised into a private entity, Railtrack, but it had to be renationalised because of a number of massive safety incidents from cost-cutting.