The majority of Londoners I know won't be affected by this change. The people I know are in council/HA flats, shared ownership flats, homeowners or paying full rent in a private rental. The only families I know out of those who get HB are the ones in council/HA flats, and their rents are so low that the caps won't affect them. Their rents won't increase because they moved into their flats years ago and the tenancy protects them from huge hikes.
There are relatively small numbers claiming HB in private rented flats. The families I know in private rented homes pay full rent themselves - there aren't many private landlords able to accept HB tenants. I have many friends working in the public sector as nurses and teachers who have shared ownership keyworker flats - London has more keyworker accommodation than anywhere else in the country.
Obviously there will be a few families who will be affected by this, but the article mentions 82,000 families, which hardly represents a huge percentage of the capital's low-paid workforce. Rents are low enough in certain parts of the capital that they shouldn't have to move out of the M25 entirely.
So it's not true at all to say that communities won't be mixed after these changes - even now, there are very poor families on benefits living on the same street as millionnaires. All of the central London boroughs have lots of council/HA tenants and they're not going to be moving out because of these caps - if anything, they'll be more likely to hold on to their tenancies and take advantage of the fact they can pass them on to their children.