Prime Minister Boris Johnson and Sir Keir Starmer have laid flowers at the entrance to the church where the MP Sir David Amess was stabbed to death a day earlier, in what police say was a terrorist attack probably linked to Islamist extremism.
The attack comes five years after the murder of Jo Cox, an MP from the Labour Party and has prompted a review of the security of elected politicians.
Amess, 69, was knifed repeatedly in the attack at about midday on Friday in Leigh-on-Sea, east of London, during a meeting with constituents.
Police arrested a 25-year-old British man at the scene on suspicion of murder, adding it is believed he acted alone.
In a statement early on Saturday, police said the early investigation had revealed a potential motivation linked to Islamist extremism.
Johnson and Starmer stood side by side in a moment of silence before leaving. On Friday, Johnson said Britain had lost a fine public servant and a much-loved friend and colleague.
As tributes poured in for Amess, politicians described the attack as an assault on democracy, and Patel said security for MPs, was being reviewed and strengthened.
"All measures are being put in place for the security of MPs so that they can carry on with their duties as elected democratic members," Patel said in a broadcast clip following the visit.
"We live in an open society, a democracy. We cannot be cowed by any individual."
In Westminster, armed police are on patrol. But in their constituencies, more often than not there is no security.
Amess was stabbed while holding a surgery - one-to-one meetings with voters, open to whoever turns up.
Conservative MP Tobias Ellwood said that while engagement with the public was a vital part of the job, there was now huge anxiety among MPs and called for a pause in such meetings.
Patel said Amess was killed doing a job he loved, and lawmakers should remain accessible to the public.
"We will continue to absolutely stand by the principles that we are elected by: to serve our constituents in the open way in which we have been doing so, but also recognising that there are safety and protection measures that we have to undertake too," Patel said.