You don't understand what a subsidy is. Offshore wind subsidies are taken out of electricity bills, not the price. The price you are seeing does not include the subsidy.

The reason why Hinkley Point is expensive is completely solvable. The reason why it is expensive is because it is supposed to be expensive, that is the purpose. An A road near me has required two lanes, so far they have spent near £100m over twenty years and have not built anything. The basic premise of the UK political system is that people have no idea what the price of anything should be because it is all a political fiction.

When the costing was done for Hinkley 10 years ago the price was going to be, iirc, something like 50% above the price of gas which was at record lows. This was regarded as extremely expensive...electricity prices are up multiples and multiples since then. Since then, you have had armies of lawyers, consultants, lobbyists, planners working on the project full-time...and you are asking why it is expensive? Thinking this requires knowing so little about how much nuclear costs around the world and having literally zero idea about infra projects work in the UK (spoiler: there is massive corruption at almost every level, tens of billions in graft every year).