That seems to confirm what I said. I am very confident on what I say, but no liability accepted (obvs!) and without searching the register myself I cannot confirm what might be missing.
Your friend owns Flat 1 on the ground floor, and they (or their predecessor in title) extended the lease on 23rd Dec 2009, by 90 years and reducing the ground rent to one peppercorn pa if demanded. This lease extension is by definition 90 extra years / one peppercorn because it says it is a 1993 Act lease extension, so it has to be 90 / one peppercorn.
This lease was then registered on 18th Jan 2010, and it was on that date, with the newly extended lease extension registered, that the original lease was "determined" (ended, and in this case superceded by the lease extension... though it is worth noting that the lease extension may be an amendment to the original lease and the original lease might still be relevant, even though the term and ground rent on the original lease are definitely no longer relevant!)
You will note that Flat 2 did not statutorily extend their lease, and whilst they have the same 189 years from 1980 as if they had extended under the 1993 act they might be paying a ground rent, and indeed they might be paying a very high ground rent. You will also note that - for some reason - their lease extension took 4 1/2 years to register which makes it look like their solicitor was not very on the ball!
On the face of it the two flat owners have a right to buy the freehold if they get together, and the cost of that freehold is likely to be (very very approximately) -
£100 # Amount down to flat 1
+
£100 # Sundries (split 50/50 between two flats)
+
£100 + £unknown # Amount down to flat 2 (with unknown being like to be in the region of £0 to £25,000 dependent on the ground rent payable)
+
£unknown # Amount down to development value (with unknown being like to be in the region of £0 to £25,000 dependent on whether the building and lease means development value is payable)
Total £300 to £50,000 (with Flat 1's share being £150 plus development value relating to her flat, which could be zero)
Professional costs can run to £6,000 easily.
The Leasehold and Freehold Reform Bill is currently going through Parliament, and if you trust the integrity and competence of the Tory government you can be confident that the cost of the freehold will come down when the law passes. I do not advocate for trusting the integrity and competence of the Tories.