Just as an aside, and after reading all of the posts in this thread...
I hope that you have adequate Public Liability Insurance!
If you start tinkering with the removal of these joists (even though you
take adequate precautions etc.) and the ceiling caves in on the downstairs
flat (hopefully while the people are out...) there'll be HELL to pay! If
they're in at the time, you might have to pay the next-of-kin!!!

Surely you could say that for just about any DIY job? There's always an
element of risk - you could plumb a bath in and flood downstairs, build a
new fence and it falls on your neighbour's dog etc etc. ...and I'm pretty
sure public liability insurance wouldn't be applicable in a case such as
this. If I were employing builders to do the work *they'd* need to have
public liability insurance.

It will also be physically impossible for the ceiling to cave in.

Also, as someone else pointed out - but I don't think you realised his
point, are you the Freeholder of your flat? You can be the owner but not
own
the Freehold - in which case you are a Leaseholder. If you are a
Leaseholder
you will need to obtain the permission of the Lessor to make the
alterations
(which you prolly won't get), and if you do there could be a clause to
"make
good" before you sell - which means putting it back the way it was
originally! That may prove difficult if you've already sold the staircase
space.

As I said, "I've checked with our solicitor and we shouldn't need the
freeholder's (i.e. the owners of the downstairs flat) consent.". It's a
standard terraced flat agreement whereby the upper flat owns the freehold to
the lower flat and the leasehold to the upper flat; the lower flat owns the
freehold to the upper flat and the leasehold to the lower flat. This
agreement is in place to simplify maintenance between the two flats etc.
It's not designed to wrap simple building work in red tape.

Andy