The key subsidy for the Hinkley Point C project is the contract for difference (CFD) which assures a stable level of revenue provided that the plant performs. The CFD, designed to provide an inflation linked "fixed" price for energy sold, is the exact same model as has been used for renewable generation in the UK for the last decade or so. The idea is that any "low carbon" energy source can utilise the same financial and legislative framework. (With some complications because "renewable" energy is exempt from state aid restrictions under EU law, whereas nuclear energy is not). The CFD is valued so as to provide an agreed level of earnings (after interest, tax, depreciation and amortization) which is typically around 10% per annum if the project were to be delivered as planned. This framework has proved highly successful for the deployment of wind, solar and biomass, as well as other projects which are classed as "low-carbon energy" such as development of district heating systems, combined heat-and-power schemes, etc.
The CFD provides, for a specified duration, a known revenue per unit production. The CFD is inflation linked, but is also linked to O&M costs and financial risks to capital costs, so factors such as a change in finance rates for debt, tax rates, as well as change in staffing, maintenance, waste disposal/decommissioning or fuel costs for whatever reason, would trigger a CFD revaluation.
While the CFD is designed to transfer macroeconomic risks to the government, it is designed to retain project risks with the project owner. The CFD has a fixed duration of operation, which will start at the scheduled date of plant commissioning. Late delivery of the project effectively shortens the duration of the CFD. There is also an option for the government to unilaterally withdraw from the CFD, in the event that the project delivery is very late (7 years).
However, having developed this framework, the UK government did agree to take on some of the project financial risk, by agreeing to underwrite loans given to EDF in relation to the project. This would protect investors from an EDF bankruptcy, although as a French state-owned company, an insolvency would seem somewhat unlikely, as I would expect the French government to step in.
That said, even the loan guarantees have a get-out clause. In the event that the plant under construction in France at Flamanville is not successfully commissioned by 2020, then the loan guarantees are void. There is a real risk that this clause may be triggered: Flamanville is in a precarious state; Areva, the plant vendor decided to bring fabrication of the reactor pressure vessel in house, instead of subcontracting it out. Whereas the external contractor (Japan Steel Works) had already produced a good quality RPV for a Finnish plant, Areva had experienced delays in upgrading their forge to do the work, and had not validated their forging process by destructive testing of a prototype prior to fabricating the RPV. Only after the RPV had been installed, and the rest of the plant built around it, was a prototype destructively tested, and found not to be of acceptable quality.