The UK Health Security Agency (UKHSA) said it had recorded 18 additional cases of the disease in England, and one additional case in Scotland.
This brings the total number confirmed in the UK to 321 as of 7 June, it confirmed.
There are currently 305 confirmed cases in England, 11 in Scotland, two in Northern Ireland and three in Wales.
A UKHSA spokesperson said: “Anyone can get monkeypox, particularly if you have had close contact, including sexual contact, with an individual with symptoms. People who are gay or bisexual and men who have sex with men remain disproportionately affected.”
The UKHSA is asking anyone with a rash with blisters who has been in close contact, including sexual contact, with someone who has or might have monkeypox in the past three weeks to contact a sexual health clinic.
It is giving the same advice to anyone with a rash with blisters who has been to West or Central Africa in the past three weeks.
From Wednesday all doctors in England are required to notify their local council or local Health Protection Team (HPT) if they suspect a patient has Monkeypox.
Labs must also notify the UKHSA if the Monkeypox virus is identified in a laboratory sample.
Wendi Shepherd, Monkeypox incident director at UKHSA, said: “Rapid diagnosis and reporting is the key to interrupting transmission and containing any further spread of Monkeypox. This new legislation will support us and our health partners to swiftly identify, treat and control the disease.
“It also supports us with the swift collection and analysis of data which enables us to detect possible outbreaks of the disease and trace close contacts rapidly, whilst offering vaccinations where appropriate to limit onward transmission.”