Writing in the Science and Technology Facilities Council's annual report for 2011-12, John Womersley, chief executive of the STFC, says that service levels at the centre remain "significantly below expected standards".
The centre was set up to bring services such as human resources, finance, IT and grant allocation for all the research councils under one roof.
Government plans to transfer the back-office functions of other bodies overseen by the Department for Business, Innovation and Skills to the centre could "add further pressure to an already over-stretched service", Professor Womersley adds.
BIS confirmed to Times Higher Education that bodies such as the National Measurement Office and the UK Space Agency would start using the SSC in the coming months.
Other organisations - including the Higher Education Funding Council for England and the Technology Strategy Board - will be considered for a similar move in the future, a BIS spokesman added.
The quality of services provided by the SSC - which include processing invoices, expense claims and grants - has been an issue for the councils since the centre's inception in March 2011.
Problems with bill payments led to a number of incidents, including a courier refusing to deliver to the STFC priceless Moon rocks from Nasa and bailiffs attempting to remove property from the Natural Environment Research Council's Centre for Ecology and Hydrology.
Sources contacted by THE confirmed that the system, although improving, remained "patchy" and was still slowing the administration of grants to "a ridiculous extent".
Internal risk assessments by the research councils themselves, outlined in their individual 2011-12 annual reports, highlighted issues including the duplication of payments and IT application security as continuing areas of risk.
However, a spokeswoman for Research Councils UK said that although there had been problems, many of those raised in the reports had since been resolved.
"There is a programme of continuous improvement in place, and the research councils continue to work closely with the SSC to ensure that any issues are resolved quickly," she said. "Many of the issues reported on...have already been resolved, and the SSC is considered close to being stable."
RCUK cited improvements including a rise in the percentage of invoices paid within five working days from 70 per cent to 80 per cent over 2011-12 and an increase in the percentage of grants launched on their due date from about 60 per cent to more than 80 per cent.
Nigel Titchen, branch president for the union Prospect at the Biotechnology and Biological Sciences Research Council, said that although members agreed that the service was improving, there were concerns that advances could be undermined by additional workloads.
With new bodies joining the centre, they worry that "they may find themselves going backwards in the type of service they receive, or that they are perhaps lower down the pecking order", he said.
In April this year, two BBSRC institutes - Rothamsted Research and the Babraham Institute - left the SSC, citing a change in governance structure and staff employment conditions that had made in-house services more suitable.
A National Audit Office report published last year found that the centre was completed 65 per cent over budget and 15 months late. It also warned that the money spent on the centre might never be recouped.
Increasing efficiency among the research councils is part of the government's plans to maintain the value of the ring-fenced science budget. Although it is protecting research spending in cash terms until 2014-15, it hopes that efficiency savings will stop the budget falling in real terms.