Since the Childcare Service launched in April, many parents have struggled to complete applications.
Parents may be eligible for a one-off payment if they were unable to log into their account, or did not receive a decision 20 days after applying.
To make a claim, parents need to fill in a form online.
Parents need to send the HMRC their full name, address, National Insurance number, bank details, copies of childcare provider receipts, and a brief description of the issues they faced when trying to apply for the childcare schemes.
Parents were required to log onto the Childcare Service website to sign up for two new government-funded childcare schemes.
They were for tax-free childcare, and the scheme for 30 hours' free childcare a week for all three and four year olds.
Under the tax-free childcare scheme, the government pays Â£2 for every Â£8 parents pay their approved childcare provider, via an online account.
The 30 hours' free childcare (1,140 hours per year) scheme is eligible to parents who are either in work or earning at least the minimum wage. The Department for Education says it is not eligible for families where "either parent has an income of more than Â£100,000".
However, since the site's inception it has been plagued by technical issues, prompting Nicky Morgan, chair of the Treasury committee and former education secretary, to demand answers from HMRC in early August.
Ms Morgan wrote to permanent secretary Jon Thompson, asking him to clarify:
HRMC apologised for the problems, saying it had now improved its service.
"We've now made significant improvements based on customer feedback, and on average more than 2,000 parents are applying successfully every single day," a spokesperson said.
The childcare service helpline is 0300 123 4097.
HM Revenue and Customs (HMRC) has begun a compensation scheme for parents unable to apply for government-funded childcare schemes due to IT glitches.