A spokesperson from a national children's charity has said the chancellor has chosen to make children "pay the price for further welfare cuts".
In the plans laid out by Osborne on 8 July, support for children through tax credits and family benefits under Universal Credit will be limited to the first two children in a family.
This means that any family which has a third or subsequent child born after April 2017 will not qualify for Child Tax Credit for that child, (which amounts to up to £2,780 a year per child).
This will also apply to families claiming Universal Credit for the first time after April 2017.
However multiple births will be excluded from the limit, so families who have triplets born after April 2017 will be exempt from the limit.
At the moment 870,000 families with more than two children claim tax credits, according to HMRC.
From 2017, to qualify for universal benefit parents of three- and four-year-olds must be in work.
As well as universal benefit working parents of three- and four-year-olds will also get 30 hours of free childcare each week, – an increase from the 15 hours they’re currently offered.
Anna Feuchtwang, Chief Executive of the National Children’s Bureau said:
"The summer budget was a missed opportunity to put children first. Apart from additional free childcare there was little that will take forward the government’s manifesto pledge to ensure every child gets the best start in life.
"It is particularly startling that the government chose not to protect the nation’s children in the same way that it is protecting pensioners.
"Cuts to welfare support have already hit children extremely hard – they are twice as likely to be living in poverty as older people.
"Yet the principal sources of support for children - child benefit and child tax credit – have not been protected with an equivalent of the ‘triple lock’ on pensions and are being reduced.
"Children deserve the same guarantees as pensioners but instead the chancellor has chosen to make them pay the price for further welfare cuts."
Ellen Broome, the Family and Childcare Trust's director of external affairs, welcomed the free childcare extension, but urged the government to ensure the wellbeing of families was fully considered when policies are made.
“The Government’s extension of free childcare is great news for working parents and will make a big difference to many families across Britain," she said.
"We are, however, concerned about the delay in Tax Free Childcare and extra support under Universal Credits, which could cost families up to £3,000 of free childcare.
"We also urge the Government to ensure that its flagship Family Test is implemented and the wellbeing of British families fully considered when policies are made.”
Anne-Marie O'Leary, editor in chief of parenting site Netmums praised the extended free childcare hours, but cautions the government will need to take steps to ensure working families will be better off than those on benefits.
"Giving mums and dads the tools to work and support their family - such as 30 hours free childcare and a National Living Wage - is a helpful move and recognises that the costs of bringing up children are still very high," she told HuffPost UK Parents.
"But changes to tax credits will have to be managed very carefully if they are not to cause hardship in some cases.
"The Government must ensure work always pays for the UK's hardworking families like Netmums members."
Siobhan Freegard, founder of young mum’s video network Channel Mum echoed O'Leary's opinion that the government needs to ensure "work pays" and adds that she thinks young families will be especially impacted by the cuts.
"There’s a real worry among young families that they’ve missed out in this Budget," she said.
"While the free childcare allowance is hugely helpful, the headline-grabbing National Living Wage only applies to over 25s, leaving younger mums and dads struggling to do the right thing by working and supporting their family out of pocket.
"Coupled with cuts to tax credits, it could even mean some of the UK’s youngest families are better off on benefits that not working, which is not what anyone wants.
"The Government should extend the National Living Wage to all staff over 18, so young families get a fair wage for a fair day’s work.
"Parents want to set an example to their children by working, so let’s see the Government set an example by treating young families the same way as the rest of the UK."
Mumsnet users have on the whole responded positively to the budget, however they have raised concern for the welfare of children born "through no fault of their own" into large families.
'We saw a lot of anxiety among our users in the build-up to the budget, with people thinking that current tax credits claims for more than two children might be affected immediately, so on the whole the response so far has been relieved and in fact pretty positive," said Justine Roberts, Mumsnet CEO.
"There is some concern about the qualifying income thresholds for tax credits being reduced, and on the whole Mumsnet users think it's important to consider the welfare of all children, including those born - through no fault of their own - to large families on low incomes.
"Life can hand out unexpected events in the form of redundancy, bereavement or unplanned pregnancy, and it's important that there should still be a safety net for those facing genuine difficulty."
Spokespeople from financial firms have also raised concerns.
Iain McMath, CEO of Sodexo Benefits and Rewards Services, comments:
"The announcement in today’s Budget that the government will be removing access to Tax Credits for families with more than two children will leave parents with a significant gap in their childcare provisions.
"The change is due to be implemented in April 2017 and coincides with the launch of Tax-Free Childcare (TFC), confirmed in today’s Budget, which will see 57% of families with three children worse off than under the current Childcare Voucher system.
"Sadly, it is those parents in the lowest income tax-bracket that so heavily rely upon these Tax Credits who are also facing severe uncertainty with the implementation of TFC.
"Our research shows that 78% of basic tax rate households will be worse off under the new scheme, compared to the existing Childcare Voucher provisions.
"Upon hearing these announcements, many parents now face a significant dilemma over their work/home balance and how they will be able to provide for the future.
"The good news behind all of this is that Childcare Vouchers, in their current form, remain available for children up to the age of 15.
"Many parents should therefore consider their position now – and certainly before the current cut off point for Childcare Vouchers in early 2017 - in order to secure a childcare solution that best serves the needs of their family.”
Karl Elliott spokesperson for mutual organisation OneFamily says that many families may not be aware of the financial support available to them aside from Child Tax Credit.
"Many families will be feeling worried by the announcement of the Child Tax Credit cap in today’s Budget," says Elliott.
"However, millions of families are unaware of wider financial policies they could be benefitting from (according to a survey 2,089 adults conducted in conjunction with YouGov)."
Elliott adds that understanding the full range of support on offer could help families offset the impact of today’s announcements.
This scheme offers equity loans and mortgage guarantees to help with the cost of a new home, and is available to first time buyers as well as homeowners looking to move. The home you want to buy must not cost more than £600,000.
Married couples made up of one non-taxpayer and one basic-rate taxpayer are allowed to share some of the non-taxpayer’s unused annual income tax allowance.
These are long-term, tax-free savings accounts for children. In the 2015 to 2016 tax year, the savings limit for Junior ISAs is £4,080.
These are available through employers and the amount you are entitled to depends on how much you earn.
You can claim this allowance if you’re widowed under State Pension age and have at least one dependent child. The amount you get is based on how much your late husband, wife or civil partner paid in National Insurance contributions, and could amount to £112.55 a week.