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Yep, totes legit. You only have a statutory right to extend a lease of a house where the lease is a 'long tenancy' as defined in section 3(1) of the Leasehold Reform Act 1967, and that means a lease 'granted for a term of years certain exceeding twenty-one years'. If this is a 21 year lease it's not a long tenancy, and there's no right to extend the lease. If the parties to the lease want to agree a lease of a shorter duration, falling outside the scope of the 1967 Act, then that's up to them.
assuming that the ground rent doesn't increase (I bet it does) you'd pay £84.5k over the 13 years. Inc the £500K that's £3850 per month. Plus I read it as you'd have to maintain The Grade 1 listed house for the duration. Then you get to give it back. At which point I assume they will sell it on another 21 year lease (it seems 21 or less years on a lease means the lease holder doesn't have the right to extend it).