Yes.
The Government contracts a Train Operating Company (TOC) to operate a train services in a defined area for a given length of time. At the end of this period the intention is to run another competition to see if an alternate supplier can offer a lower subsidy/higher premiums/higher quality service for the next period.
The given length of time for a franchise (more correctly called a 'concession') is usually for a period of between seven and ten years. This is much shorter than the expected life of the rolling stock which is usually expected to last between thirty and forty years.
The Rolling Stock Companies (ROSCO) were therefore created to own the rolling stock for the whole of its life. They started life owning the ex-BR stock, the bulk of which has since been scrapped. The present value of the stock which has been purchased since then is somewhat north of £10 billion - this does not include the trains contracted by the Department of Transport under the IEP and Thameslink contracts. These latter two train types were financed by the manufacturers, estimates give the present value of both fleets to be around £3.5 to £4 billion.
The TOCs lease the trains from the ROSCOs.
End of story.
I would add that since making the private sector responsible for the procurement and ownership of the trains there have been a number of consequences:
- It enabled the Government to deem slam-door stock to be unsafe and demand that it be removed from service prematurely. This was possible because there was no cost to the Government - ask yourself if the Treasury would have funded a large number of trains to meet an artificial, DfT imposed deadline
- Ask yourself if the Government would have committed itself to a deadline for the Persons of Reduced Mobility modifications to be made to the rolling stock if it itself had to pay (No other Government in the EU required existing stock to be modified)
- Ask yourself if there would be as many trains available as there are at the moment if the Treasury had to fund their construction.
To add some meat to my points above. Governments are always under pressure to spend money - they have only one source of income (various taxes) and there are incessant spending demands for both ongoing (pensions, health care, education, local government, police, civil service wages and salaries, etc., etc.,) and capital spending on all those parts of the national infrastructure for which the Government is responsible.
Historically railways have always come way down the list of priorities.
Edit: Added last sentence for context to railways.