"can I afford a 3rd baby", who've sat on trains an hour each day, these are the people who would have to pay more tax to stop benefits from being capped which will push poorer people out of the city. The Tories won because they won over people like this."
No - that's simply not true.
There are not many families on benefits who will be severely affected by the benefit cap as most UK families have fewer then 2 children.
In areas where it has been piloted very little money has been saved, as the cost to councils of social services input, and rehoming families who were evicted after falling short on rent due to the cap has cancelled out most of it. Only a tiny percentage of those who were affected by the cap have increased their hours at work or moved into work, regardless of the impact of the cap on their families.
The benefit cap is about punishing people who are deemed lazy, and making a point, not about saving large amounts of money.
Quoting from here
"Of the 42,000 households getting more than £500 per week in benefits in May 2013, about 2,000 had someone in the house get a job over the following 12 months in response to the cap."
As the Institute for Fiscal Studies put it, “… the large majority of affected claimants responded neither by moving into work nor by moving house”.