There are several high-profile sports events in Britain in the coming weeks, including the FA Cup final at Wembley on Saturday, although there is no specific threat.
The Islamic State extremist group claimed responsibility for the bomb attack at the end of a concert by US pop star Ariana Grande at the Manchester Arena on Monday.
Britain's deadliest terror attack for 12 years took place just two days before Manchester United's Europa League final against Ajax in Stockholm.
Wednesday's game is still set to go ahead and UEFA, European football's governing body, said that "tight security arrangements" had long been in place.
"There is currently no specific intelligence which might suggest that any of the UEFA Europa League final activities in Stockholm may be the target of attacks," said a statement.
"Furthermore, a number of additional security measures were implemented following the attacks in Stockholm last April (when a hijacked truck killed five people)."
The statement urged fans to get to the stadium early for "detailed checks".
London's Metropolitan Police said that extra armed officers would be deployed for the FA Cup final between Arsenal and Chelsea at Wembley and the English Premiership rugby union final between Exeter and Wasps at Twickenham.
Golf officials were meeting security experts ahead of this week’s flagship European PGA Championship event at Wentworth, southwest of London, on Thursday.
"As with any major event, security is the highest priority," Keith Pelley, the European Tour chief executive, told reporters at Wentworth.
"It was before last night and it remains so. We're in constant dialogue with the police and security services.
"We have several meetings later on this afternoon but we are comfortable we will react the right way if in fact we need to significantly increase our security."
Britain's Chris Wood, the defending champion of the event, added: "It's horrible. I have a three-month old (child) now and it hits harder when you know children are involved.
"It's a very sombre feeling (in the locker room) and golf seems fairly insignificant."
At a hectic time for sport in Britain, next week sees the start of cricket's Champions Trophy tournament involving the world's top eight one-day international sides, with matches in London, Birmingham and Cardiff.
The International Cricket Council said it too was looking at tighter security.
"We will continue to work with authorities over the coming hours and days and review our security in line with the threat levels," a statement said.
Before then, hosts England and South Africa are involved in a three-match ODI series starting at Headingley, in Leeds, on Wednesday.
South Africa team manager Dr Mohammed Moosajee said his players had "some genuine concerns" over their safety, with the Proteas set to remain in England until early August on a tour that also includes a four-Test series.
However, speaking at Headingley on Tuesday, Moosajee told reporters: "There have been guarantees put in place that security arrangements will be supplemented, starting today."
England one-day captain Eoin Morgan said cricket would not be daunted.
"I'm confident that we will crack on," he said.
"It certainly does put things in perspective for everyone in the country and around the world.
"When it happens so close to home it hits you a little bit harder."