I think formally Network Rail owns most of the railway infrastructure, and operates it under licence to ORR.
DfT ultimately owns or at least funds Network Rail, and in effect controls it.
Some railway infrastructure has other owners, eg: TfL, Heathrow Airport, Eurotunnel, Eurostar, port authorities, PTEs, private sidings/terminals etc.
HS1 is owned directly by the government (but operated and maintained under contract by NR) and its traffic rights are held privately on lease.
Something similar is planned for HS2 when it is operational.
TOCs lease their stations from NR as part of franchise agreements, but NR runs major stations directly.
There are some complex situations like Crossrail core and the ELL where (I think) TfL owns the infrastructure but NR provides the signalling.
At the margins, not all of this infrastructure is in public ownership.
As part of the review of railway organisation, the government is looking at different ways of funding Network Rail.
The infrastructure companies (eg the signalling majors) may well have part-ownership of route upgrades going forward.
So "ownership" may get more complicated rather than less.
New stations tend to be funded locally (often with a government grant), so are not wholly in NR ownership.
Recent examples are Kenilworth and Worcestershire Parkway,
The devolved authorities have also sometimes taken over railway development (eg the Scottish Government for the Borders line, and the Welsh Government for the Ebbw Vale line).
The Cardiff Valleys lines are due to transfer from NR to WG prior to their upgrade and electrification.
The East-West Railway is also likely to be separated from Network Rail and may have a different ownership in the future,