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If the lawyers are not complete numptys then you are half way there imo.
One thing that personally I'd be checking very carefully about your new place (which I like) is the service charge and the management of the block. There might be service charge fun and games going on. My mate lives in a similar sort of block in Bow (where I used to own a flat- I sold it as the service charge was 3k and climbing and its now over 4k) . He got fed up of it all and managed to wangle his way onto the management committee to sort it all out. I'd personally be going through the accounts with a very fine toothcomb to make sure there isn't any madness going on which will stress you out later.
I do have a little bit of experience of going through these accounts from when I was getting rodded during my leasehold ownership experience, so if you want a second opinion on the accounts when they send them to you as part of the information pack then feel free to dm me and I'll take a look. I know you said you used to live in the block so you might already know its all cool.
You any closer to buying your new place?