Not so. LCR was originally a private company that won the right to build CTRL. It was privately held from 1994 until 2008 when the government acquired it for a nominal sum because it was essentially bankrupt and the DfT had previously guaranteed its debt through issuance of government bonds. What part of government owns it isn't really a question, all state owned property is owned ultimately by the Crown, and responsibility over assets can be transferred around with the stroke of a pen. LCR is managed by the DfT and SecState for Transport. Since nationalisation, CTRL was sold off, and subsequently it has been used as a Quango/Development Company for various rail projects. Waterloo International was owned by BRB Residuary (a DfT state owned company), dissolved in 2013, at which point Waterloo International was transferred to LCR. LCR also has or had ownership over parts of HS1, Kings Cross redevelopment and Stratford International.