Both Oxfordshire County Council and Oxford City Council have removed their websites from service while investigating a technical problem described as a known global issue.
The National Cyber Security Centre linked the disruption to a critical security vulnerability affecting the programming language PHP.
Organisations operating websites built with PHP were advised to introduce temporary safeguards or withdraw affected systems until updates could be applied.
The US cyber security agency said such weaknesses can give attackers direct access to a server’s file system or database.
Several public-sector and media websites have been affected, including the Finnish Government’s website, the Netherlands’ cyber-security agency, parts of Wikipedia, and online pages for BBC programmes such as Doctor Who and The Traitors.
Oxfordshire County Council took down its main website, which normally provides access to parking and traffic-filter permits, library accounts, information, care services and community support.
A temporary website was introduced to cover urgent matters, including safeguarding, schools, permits and HWRC bookings.
The council said its usual web address would redirect users to the temporary site, while the contact centre remained available on 01865 519800 for urgent issues.
Callers were warned that demand could be high and advised to try again later for anything non-urgent.
Before the replacement site was launched, visitors to the main address encountered an error and a Google warning that attackers might attempt to steal information such as passwords, messages or credit-card details.
Oxford City Council also took its website offline.
The site normally handles council-tax payments, business rates, planning applications, housing, bin collections and leisure services.
In a social-media update, the council explained that the closure was a precautionary response to a worldwide technology problem rather than a cyber incident.
Telephone enquiries remained possible on 01865 249 811.
The National Cyber Security Centre said every version of PHP was affected and urged organisations to install the latest fixed release.
Operators of older versions were also advised to move to a fully supported version.