The Inland Revenue has dismissed reports the new tax credits system is in chaos leaving millions of families short of money.
Nine out of every 10 families with children should benefit
A spokesman said the one out of every four families that opted for weekly payments could receive an emergency interim payment from their local tax office - but the vast majority had already been paid.
Families that opted for monthly payments should be paid by 2 May, according to the Revenue - but families that applied after 31 January may not be paid on time.
But BBC News Online has been inundated with e-mails from families who say they are facing hardship from delays in processing their payments - and can not get through to the helpline.
Almost one out of every 10 of the 5.75 million families entitled to claim have failed to do so.
Help for families
Nine out of every 10 families with children, including all households with an income up to £58,000, will benefit from the Child Tax Credit and Working Tax Credit, according to the government.
But the claim forms, which only went out in late August, have been criticised for being confusing.
Two thousand staff had been expected to work on a new telephone helpline - but because of the huge demand an extra 700 workers have been re-deployed and trained to answer phone inquiries.
Father-of-two Ted Duggan, from Coventry, is just one of the many people who contacted BBC News Online.
Mr Duggan, whose wife died from leukaemia three years ago, said the tax credit was vital for him to support his family.
Despite applying well in advance, his application has yet to be processed.
He said: "It hasn't been easy since my wife died. What with this pressure on us, we do not need it."
Call for an inquiry
Conservative work and pensions secretary David Willets said "the so-called helpline" had collapsed.
And millions of families would not get the money they had been promised.
"People either cannot get through at all or they are faced with a 20 to 30 minute wait.
This is a recipe for confusion and chaos
Liberal Democrat work and pensions spokesman Steve Webb
"The idea people will have to queue at tax offices to get Giro cheques demonstrates the woeful failure of this entire enterprise.
"This is just a shambles."
Liberal Democrat work and pensions spokesman Steve Webb BBC News Online said there should be an inquiry.
He called on the Revenue to prioritise payments to low-income claimants - people who were receiving Working Families Tax Credit and Disabled Person's Tax Credit.
"To them it is a central part of their income...it is their bread and butter", he said.