Happysnapper
Goodluck.
In a totally private block the freeholder is legally bound to insure the buildings for all the leaseholders plus the communal areas. They would then charge this pro rata to the leaseholders. Your contents would be up to you.
Surely the same applies to Lewisham Homes. They would insure the whole block and debit you pro rata. You seem to be saying you are insuring your flat for buildings insurance or have I got that wrong. I did not think Insurance companies did this as the whole block would need to be insured with the same company.
Of course could be Lewisham Homes do not insure as they have many properties and therefore act as there own insurer?
Good Luck anyway.