By Paul Lewis
BBC Radio 4's Money Box
The government minister in charge of tax credits has admitted that the payment system "has not worked 100% right from the word go".
Treasury Minister Dawn Primarolo has promised to look into cases where people applied on time but have still not received their money.
Tax credits should have been paid in the week of 7 April. But many people have contacted the BBC to say that they have not received their payment on time.
Tina lives in Dudley and works part-time to support her two children and her disabled husband.
She should receive £115 a week in tax credits. But although she applied at the start of February when she began work she has still not had anything.
"I was getting £115 a week on top of my wages," she said.
"But now all I've got is my part-time wages of £67.20 to keep a family of four. All I'm doing is grocery shopping.
"I've put my rent on hold for a month and the water board has put my account on hold for a month. It makes me feel like a bad payer but I'm not.
"I've always paid my bills on time. But when your money's not coming in you have to prioritise and I have to put my children first, I have to feed my children.
"I enjoy my work and like the independence but at the moment I'd be better off not working because at least you get your benefit every week coming through."
Ms Primarolo told BBC Radio 4's Money Box programme: "If we take the case of Tina she is absolutely right to be angry with us for not having received her money yet and we need to look at that urgently and get her payment made to her to ensure she can meet her obligations."
I can't put my hand on my heart and say the system worked 100% right from the word go
Treasury Minister Dawn Primarolo
But the minister stressed that more than one million weekly payments were being made and that another two million would go out next week to people who had chosen to be paid monthly.
Another 1.3m people were getting extra money with their existing benefits.
"If you've got 4.3m people who are already receiving or about to receive next week, that's a lot of people," she said.
"But I can't put my hand on my heart and say the system worked 100% right from the word go."
So would people who were paid late get compensation? After all, if we send in our tax return late then we are fined £100.
Would Tina and others still waiting for money they desperately need get payments of £100?
Ms Primarolo said: "There are many, many people who are getting an excellent service, millions are receiving their money.
"Some haven't and we need to address that as quickly as we can. We need to make sure that we have given them the service they are entitled to and, if they haven't been given that service, what redress we can make to them."
The Inland Revenue is operating an emergency payment system.
Anyone who is still waiting for their money can go to any Inland Revenue inquiry office with identification and, if possible, the documents showing their old tax credit awards from last year as well as any documents relating to their application.
The office will then make an emergency payment. The process can take an hour or so.