Armed officers were on duty at Leeds railway station and were also seen around nearby City Square.
Patricia Chapman, from Pudsey, was at the station to meet her daughter as she celebrated her 75th birthday.
She said it was a shame armed officers were needed because of the national situation.
“It is a bugger when it comes to this. I think it is good to have it and is reassuring, especially for older people.
“But is sad it has come to this. You never had this when we were kids, people could walk about safely and leave their doors open.
“It is terrible. I fear for younger people like my own grandchildren.”
She said the events in London make her grateful her own family are safe and well.
William Grayson, aged 86 and from Armley, said he doesn’t want to see all police officers being armed as “I don’t like guns and it would be like America”.
But he added he appreciated why armed officers are needed given the events in London.
“You can’t understand people about like that doing those things. I go could go out with my kids and get shot dead, it is not nice.
“I was disgusted when I saw the news, it is shocking.”
Julie Harrald, aged 52, said there had been an extra police presence across the region as she travelled by train to Leeds from Long Eaton in Derbyshire.
“You can’t always tell if they are armed or not but it is good to see them.
“They look like the eyes and ears of the force. It was clearly just a presence which is fine.”
At Leeds Council, there was a minute’s silence ahead of meetings for the victims of the London attack.
Flags were flying at half mast last night at Leeds Town Hall and Leeds Civic Hall.
Other civic buildings in the city are following suit today while the same mark of respect is being paid by Sheffield City Council, Rotherham Council and Doncaster Council.
Firearms officers were stationed in visible positions across Yorkshire, with more armed response vehicles than normal on duty.
West Yorkshire Police’s Assistant Chief Constable Russ Foster urged the county’s residents to be “alert but not alarmed” as the force works to protect their safety and security.
ACC Foster said: “At this time there is no specific information suggesting an imminent threat to West Yorkshire and there has been no change to the current threat level for international terrorism in the UK which remains at Severe and which means ‘an attack is highly likely’. We will continue to review our deployments and take all possible steps to keep people safe and minimise the risk of a terrorist attack occurring.
“The public will see an enhanced policing presence across West Yorkshire as the UK police together with security and intelligence services are working around the clock to help keep communities safe. This will include increased visibility of uniformed officers and an uplift in the capability of armed response vehicles”
Andy McDyer, Assistant Chief Constable at Humberside Police, also promised an “enhanced policing presence” across East Yorkshire and North Lincolnshire, with uniformed officers more visible.
Anyone who has any concerns or sees anything suspicious is asked to report it immediately to the Confidential Anti-Terrorist Hotline on 0800 789321 or dial 999 in an emergency.