"BAE has said that they don’t know the exact cost of building such a ship in the UK."
To be absolutely fair to both parties (BAeS and MoD), this month is the 27th anniversary of the last time it was MoD Air Systems policy to know the "fair and reasonable" cost of anything, followed swiftly by the policy of the Services not quantifying a requirement. Some did it, others didn't; the point is it was no longer deemed necessary. If you don't quantify, you can't cost. I have a very good friend in DE&S who is a 1 Star and nearing retirement. He cannot remember these old policies. What chance do newer recruits have? They have my sympathy.