The UK Health Security Agency (UKHSA) said the new cases bring the England total since May 7 to 85, and the UK total to 90.
Health officials in Wales confirmed their first case on Thursday morning, before the Public Health Agency in Northern Ireland later confirmed a case.
Two further cases were confirmed in Scotland, Public Health Scotland said, bringing the number of cases north of the border to three.
People with unusual rashes or lesions, particularly if they have had a new sexual partner, have been urged to limit their contact with others and contact NHS 111 or their local sexual health clinic.
Dr Susan Hopkins, UKHSA chief medical adviser, said: “We are continuing to promptly identify further monkeypox cases in England through our extensive surveillance and contact tracing networks, our vigilant NHS services, and thanks to people coming forward with symptoms.”
Dr Giri Shankar, director of health protection for Public Health Wales, said: “We are working with the UK Health Security Agency, Public Health Scotland, and Public Health Agency Northern Ireland, and we are ready to respond to cases of monkeypox in Wales.
“The case is being managed appropriately. To protect patient confidentiality, no further details relating to the patient will be disclosed.
“Everyone is being asked to be aware of the monkeypox symptoms, but it is important that gay and bisexual men are alert as it’s believed to be spreading in sexual networks”.
Dr Gillian Armstrong, head of health protection at the Public Health Agency in Northern Ireland, said: “Following the detection of cases of monkeypox in England, the PHA has been in regular contact with UKHSA regarding the situation and we established a local multidisciplinary incident management team (IMT) to ensure that we are fully prepared for any potential risk to the population of Northern Ireland.
“The PHA has been working closely with trusts and GPs to raise awareness of the disease, and set up testing arrangements and clinical pathways.
“Cases of monkeypox are rare as the virus does not spread easily between people; therefore the risk to the Northern Ireland population is considered low.
#Monkeypox Anyone with unusual rashes or lesions on any part of their body should contact NHS 111 or call a sexual health service. With recent cases mainly reported in gay and bisexual men, those in this community should be particularly alert.
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— UK Health Security Agency (@UKHSA) May 23, 2022
“Appropriate public health actions are being taken and the PHA is working with UKHSA to investigate any potential links with UK cases and we will contact any potential close contacts to provide health information and advice.”
In Scotland, the two latest cases are said to be in people with “recent travel history” and they are being treated in line with nationally agreed protocols and guidance, according to Public Health Scotland.
The agency’s medical director Dr Nick Phin said it was working with NHS boards and others “to investigate the source of these infections”.
He said: “We have well-established and robust infection control procedures for dealing with such cases of infectious disease and these are being strictly followed.”
Despite the rise in cases, the UKHSA has said the risk to the overall UK population “remains low”.
Gay, bisexual and men who have sex with men are being urged in particular to be aware of symptoms, especially if they have recently had a new sexual partner.
UKHSA teams have been tracing contacts of those with a confirmed case and are advising those at highest risk to isolate for 21 days.
A smallpox vaccine is also being offered to close contacts to reduce their risk of symptoms and severe illness.