The latest cases bring the total number confirmed in England since May 7 to 101.
There have been three confirmed cases in Scotland, one in Wales and one in Northern Ireland, taking the UK total to 106.
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.
Despite the rise in cases, the UKHSA said the risk to the UK population “remains low” as the virus does not spread easily.
Men who are gay or bisexual and men who have sex with men are being urged in particular to be aware of symptoms as the health body said “the majority of the cases identified to date” have been among this group.
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.
“We are asking people to look out for new spots, ulcers or blisters on any part of their body. If anyone suspects they might have these, particularly if they have recently had a new sexual partner, they should limit their contact with others and contact NHS 111 or their local sexual health service as soon as possible, though please phone ahead before attending in person.”
The first cases of the virus in Wales and Northern Ireland were recorded on Thursday, while Scotland confirmed a further two cases.
UKHSA teams have been tracing contacts of people with a confirmed case and are advising those at highest risk to isolate at home for up to 21 days.
A smallpox vaccine is being offered to close contacts to reduce their risk of symptoms and severe illness.
