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The head of Britain's National Crime Agency (NCA) said on Monday that there is "no indication of a second surge of cases (cyber attacks) here in the UK", but that does not mean there won't be one.
The spread of the ransomware, known as Wanna Decryptor, has affected over 150 countries. The ransomware encrypts files on a user's computer, blocking them from view and demanding a payment to release them.
In Britain, many National Health Service (NHS) organisations have been hard hit by the cyber attack, with daily work being disrupted.
"The NCA is leading the criminal investigation into the attack, but for operational reasons we cannot give a running commentary," said Lynne Owens, general director of NCA, in a statement.
"We're trawling through huge amounts of data associated with the attack and identifying patterns," she said.
The NCA has provided guidance on how to avoid falling victim to the ransomware, and has sought collaboration with international partners.
"More than 150 countries have been affected, and we're in constant communication with international partners, including Europol, Interpol and the FBI and the collaboration has been strong and effective," said Owens.