Those complaining about HSE statistics – they come from actual accidents reported by workplaces in England and Wales.
So all of those 600 falls down stairs will have been work related and will therefore exclude the (presumably many more) falls down stairs outside of work.
That said, 600 seemed high to me so I took a quick look:
For non-domestic stairs, it is estimated that each year in the UK, there are over 100,000 injuries
(DTI, 1999 cited in Roys & Wright, 2003) and around 100 fatalities (Office of National
Statistics, 1996/7/8 cited in Roys & Wright, 2003).
During 2001/2002 there were 500 RIDDOR reported accidents involving low falls (below two
metres) from stairs. For this time period, this made stairs the second most significant agent in
low falls behind ladders. The majority of these falls result in over 3 day injuries although a
significant portion involves major injuries.