The two-child cap was introduced by Conservative chancellor George Osborne and it applies to third, or subsequent, children born after 6 April 2017.
A total of 1.6 million children are living in larger families who cannot claim these means-tested benefits as a result.
If the cap had not been introduced, affected families could have received an average of £4,400 in benefit entitlements a year, roughly a tenth of their total disposable income, according to the Institute for Fiscal Studies.
Rachel Reeves has suggested she favoured removing limits on benefits linked to family size in this week’s Budget.
The chancellor previously told the BBC it was not right that children in bigger families were “penalised” through “no fault of their own”.
Caroline Goodwill, a manager at the Scholemoor Community Centre, which Ms Begum attends, said there were families that would “benefit greatly” from the cap being lifted, but she could “see both sides of it”.
“Some people will think mums are having kids so they can claim more benefit,” she said.
“But I think it would help a lot of children in this area where families are struggling.”
Ms Begum said lifting the two-child benefit cap “would help, not just myself but a lot of people out there that are struggling and who don’t want to say they’re struggling”.
“You would like to save a little for your child for a rainy day just in case you need something. It would be really great if they do lift it,” she said.
