Plus your underestimating the government's interest in the shipbuilding industry.
That's what I don't get. Constantly building ships means all the associated economic activity and therefore all the taxes coming back to the Crown.
But, and hear me out, what if the government bought fewer ships, thereby saving money, and got private companies to compete for individual contracts, thereby forcing the prices as low as possible? No, it doesn't work. But to the Treasury, it makes perfect sense.
The fundamental problem with the UK - and not just in defence - is the deep-seated political belief that the government shouldn't spend money on things. Pick a random government department or project, and you're sure to find the signs of underinvestment and an obsessive focus on in-year spend.