Legal Adviser specialising in housing law, specifically around homelessness. I have advised thousands of homeless households over the years.
A household would be classed as 'homeless' if they were statutorily overcrowded. It is very difficult to be classed as stat overcrowded because the number of people who can share a space legally and the types of rooms that are classed as suitable to live in mean most people are either clearly just about ok.
Those properties I've seen where they are stat overcrowded are absolutely dire and certainly no place for a child.
Whilst I can't say for definite that those who are statutorily overcrowded aren't included in this 100,000 statistic (since they would be counted in the DCLG's homeless stats) if they are, they will make up a tiny proportion. As above, I find their case no less compelling because the conditions they live in are simply appalling.
People will not be included in these stats just because they have children sharing a room. You might, perhaps, be thinking along the lines of the (much misunderstood) 'rule' about children over the age of ten being 'entitled' to a room each. A woman with two kids aged 8 and 15 would in a two bed property would not be stat overcrowded.
Shelter are absolutely amazing and do so much work not only to raise awareness about the abject misery that thousands upon thousands of vulnerable people find themselves in, they give fantastic legal advice for free and advocate until they're blue in the face for their clients.
Trust me when I say that things in the world of housing & homelessness right now are terrifying- I advise people, many of whom with kids, many of whom who have decent incomes, who find themselves homeless and battling against the odds to try and get help.
If there were ever a charity requiring your support, it's Shelter (and no, i promise i don't work for them!)
Should you still be unsure, I am more than happy to answer any questions you might have about homelessness.