A serious Flaw in the design of Intel's chips will require Microsoft, Linux and Apple to update operating systems for computers around the world.
The UK's National Cyber Security Centre (NCSC) said it was aware of the issue and that patches were being produced.
Some experts said a software fix could slow down computers.
"We are aware of reports about a potential flaw affecting some computer processors. At this stage there is no evidence of any malicious exploitation and patches are being produced for the major platforms," the NCSC said in a statement.
"The NCSC advises that all organisations and home users continue to protect their systems from threats by installing patches as soon as they become available."
The bug could allow malicious programs to read the contents of the so-called kernel memory of computers, which can include passwords and login keys.
Experts advised caution on the issue.
"It is significant but whether it will be exploited widely is another matter," said Prof Alan Woodward, from the University of Surrey.
"The actual flaw is being rather tightly kept under wraps but from what researchers have gleaned themselves, it's all to do with a flaw in the way certain Intel CPUs address certain types of memory.