Well, if say, the Type 31 and 32's were churned more frequently than frigates would have been in the past and a service life of 20 or so years followed by disposal, ideally on hot transfer to allied powers, then you might easily see enough numbers running to keep a construction industry running. It'd also be cheaper -with a fleet of relatively young ships, you can skip the expensive refits and repair bills at the end of their expected lives for instance.
We've seen how hard keeping ships on for 30 plus years can bite - the oldest in the fleet are always the most expensive, year on year.
I do think if someone presented a solid economic case on the benefits of serial production, yards constantly running, which reduces costs, the lack of need for as much complex refit work, higher availability - something that an accountant can get behind, then it would be possible.