By Alistair MacDonald and  Christopher Whittall

LONDON—Prime Minister Theresa May, who spent six years in charge of the U.K.’s interior ministry, is facing her first major test handling a security crisis since becoming the country’s leader following the Brexit vote.

Days before she is set to formally start Britain’s exit from the European Union, Mrs. May will have to juggle the fallout of the deadly attack Wednesday at the heart of the government as she guides the nation through a historic transformation.

After a suspected terrorist ran over pedestrians and attacked a police officer, Mrs. May was hustled from Parliament to Downing Street, where she conducted an emergency meeting with top officials. Some six hours after the incident, Mrs. May described the attack as “sick and depraved” and aimed at the heart of democracy.

“We will move forward together, never giving in to terror,” she said, speaking outside 10 Downing St.

Mrs. May’s long tenure as home secretary puts her expertise in the spotlight. While some critics argued she sometimes places concerns about personal liberty over security, she also oversaw sweeping increases in surveillance powers of the security service.
“No prime minister…has been better prepared to deal with this [attack] given her responsibilities for six years looking after these very issues,” said Anthony Seldon, an expert on British political history.

Mrs. May was the U.K.’s longest-serving home secretary in modern times. She took the role in 2010 and left it in July when she became prime minister.

As home secretary, she was in charge of British police, border security and the domestic intelligence services MI5.

“She’s absolutely smart and strong on security,” said Jonathan Russell, head of policy at Quilliam, a counter-extremism think tank in London.

Last year, Mrs. May helped the government push through an overhaul of spying powers that will require communications companies to keep records for a year of every website and messaging service that individuals have accessed. The policy leaves the U.K. with more electronic surveillance powers than almost any other Western country, experts say.

But during her tenure, the Home Office budget was subject to cuts amid a wider austerity measures: As a percentage of the U.K.’s overall budget it fell to 1.6% from 2.7%. Policing took the brunt of those cuts, with staffing levels falling by almost 20% between 2010 and 2015, according to the Association of Police and Crime Commissioners. Current plans could push police staffing levels to their lowest level in 50 years by 2020.

Intelligence agencies were spared the deepest cuts. As a share of the total budget, intelligence funding did drop slightly under Mrs. May, but the money available rose in 2016 compared with the year Mrs. May took office.

The Home Office declined to comment for this article.

Some analysts said critics may also go after measures she took in the early part of her Home Office tenure that they say made U.K. law enforcement less intrusive for terror suspects. That included ending the use of so-called Standing Orders, which restricted where a suspect could travel.

“She was the home secretary that said the balance between liberty and security had to be recalibrated to liberty,” said Anthony Glees, professor of Politics at the University of Buckingham. Mr. Glees said that people would judge British intelligence if the suspect had left a trail.

“Then we will be able to make a judgment on how much should have been known,” he said.

Mrs. May is set next week to trigger the mechanism starting Britain’s exit from the EU. Some wishing to stay in the bloc and former senior intelligence officials have argued that Brexit could hinder police cooperation and cross-border investigations.