Not really down to care home death not being recorded correctly, its the lag (which is weeks) in the deaths being registered and the ONS publishing the figures.
The FT aren't plucking figures out of thin air, they're looking at the existing published data and then using that to model the numbers for the more recent period where the data is not yet available. The person behind this, Chris Giles, has said several times on twitter that they are deliberately being conservative with their modelling to avoid panicking people with a large number that turns out to be too high.
There is a methodology behind it which is explained here:
UK coronavirus deaths more than double official figure, according to FT study | Free to read
or a shorter explanation in this thread: