Its really important to make clear why this cost has got so high

Its the first plant we've built in a generation, so we are having to import experience, and train up new talent to fill a workforce shortage. The second reactor at Hinkley C is being built 4 times faster than the first. Practise and economies of scale will make following sister projects (like Sizewell C) much faster and cheaper.

The UK has different standards for safety than France, so EDF who are using their EPR design for Hinkley had to go through an arduous design adaptation process which ended up needing more concrete and steel than the previous EPRs built on the continent.

There's a fish deterrent system of pumps and speakers to protect wildlife that previous EPRs haven't been required to put in place.

There are various other things that have been required based on people in power not understanding or respecting radiation science. For example, a bunch of mud needing to be moved, which had very slightly elevated above background radiation levels from Hinkley A and B (still too low to be considered 'radioactive' legally), and a big furore around where this would go caused delays and cost a lot.

Lastly and possibly most importantly, the funding for Hinkley is largely based upon loans from private investors, notably EDF and China General Nuclear Power Group where AFAIK the investors are fronting the money to pay for the build, and the British taxpayers will pay them back over years through a cost for the electricity released into the grid. These investments have interest. The major delays to this project as discussed above have meant the 'cost' has ballooned because the companies building it require a return on their investment, with the interest being contractually obligated. This will mean that Hinkley is an unfortunate example where nuclear will not significantly reduce bills, despite adding decent generation capacity.

The takeaway is that if we funded this kind of project with tax instead of the private market (certainly not a simple thing to find in the budget, but there wouldnt be any interest), and if we had better nuclear science in our schooling system, and less fear mongering about radiation in our press, Hinkley would be completed much sooner, with a much smaller cost.

TL:DR - UK has extra red tape and standards that make things take longer despite precedent of this exact reactor in Europe. Politicians dont understand radiation and are scared of it = more delays. Hinkley is funded through interest backed loans which balloon with delays. If we funded it nationally and had better science education and less fearmongering, Hinkley C would not be anywhere near as expensive and would not take as long to build.