The UIS does not provide a general service for registering domains
under ac.uk on behalf of institutions, although it will do this if
it is required for another service provided by the UIS (for example,
if the UIS are providing a website for www.project.ac.uk, we will
handle the registration and renewal of this as part of this).
Institutions or groups within them that require a domain directly under
ac.uk should contact a registrar who can provide such a service and
gateway their request to Jisc (who manage the ac.uk namespace). One
such provider is Mythic Beasts.
(The UIS previously offered the 'Managed Zone Service (MZS)' which did provide this but this was closed down in October 2021 and all domains transferred to customers under Mythic Beasts, who are free to move the domains again, if they wish.)
As such, the information provided below is guidance for making an application this will be discussed more completely by the registrar.
Jisc has a naming committee that approves ac.uk domain
registrations, and they require some supporting documentation to
justify the name. The ac.uk domains that are registered are
typically projects that span multiple higher education / research
institutions.
The eligibility policy for allocating domain names under
ac.uk mostly classifies various kinds of research and
education institutions; the ac.uk domain registrations that we
see are typically special projects that fall into the other
catch-all categories (points 3.p and 3.r of the policy).
For most applications, the supporting documentation is covered by point 5.c of the policy, i.e. a description of the project, which organizations are involved, and some information about how it is funded. If you have an existing web page with that information, then you can include a link to that page.
It usually takes about a week to get approval, though Jisc's policy allows them to take longer.