Military personnel have been deployed to free up officers for patrols over the weekend following the decision to raise the threat level to critical, meaning another attack is expected imminently.
In Yorkshire, there is a heavy armed police presence at the St Leger Festival, at Doncaster Racecourse, with body and bag searches carried out on everyone entering the venue.
Robin Smith, British Transport Police Assistant Chief Constable, urged the public to be "alert but not alarmed" and report any suspicious behaviour.
He told the Press Association: "Code critical is a well-rehearsed plan now, regrettably of course.
"What the public can expect to see is a lot more officers, a lot more police officers, a lot more armed officers, throughout the stations.
"Not only in London - although we are focusing on the London Underground - but also across England, Scotland and Wales."
He urged the public to remain vigilant, adding: "I think people know when things are suspicious.
"They should be alert but not alarmed."
Metropolitan Police Assistant Commissioner Mark Rowley said on Friday that extra officers would be on patrol and security would be reviewed at events across the country over the weekend.
He said: "Military personnel have been drafted in to protect national infrastructure sites, allowing additional armed police officers to carry out patrols.
"Communities across the UK can expect to see more officers, both armed and unarmed, on patrol by foot and in vehicles over the weekend. In particular, they will be patrolling at crowded places, iconic sites, transport hubs and ports."
Mr Rowley, the UK's most senior anti-terror police officer, also urged communities around the UK to be vigilant and report any suspicious behaviour to the police immediately.
"Please do not hesitate, no matter how insignificant you may think the information you have is - please let us decide. It could be crucial," he said.
Announcing the raised threat level, Theresa May said police had asked for authorisation to enact part of the first phase of Operation Temperer - "a well-established plan to provide military support to the police".
Operation Temperer is being enacted after security experts warned another terrorist attack could be imminent.
The use of the military is believed to allow up to 5,000 troops to be deployed in support of the police.
The plan was activated for the first time on May 23 following the Manchester Arena bombing when the Prime Minister said the police had asked for military support and the request had been approved by Secretary of State for Defence Sir Michael Fallon.
At the time, soldiers were stationed at sites including Buckingham Palace and the Houses of Parliament, allowing additional armed officers to attend events such as the FA Cup Final.
Meanwhile, London Mayor Sadiq Khan also urged people to be vigilant, further confirming that additional officers, including armed officers, would be on the streets.
He wrote on Facebook: "There will also be some military personnel deployed to guard sensitive sites which are closed to the public. Meanwhile, on our transport network, extra staff will be on duty and visible."