Security will be "intensified" at events in major cities and at UK borders in the wake of Friday's terror attacks in Paris, Theresa May has said.
Security plans will be reviewed and any necessary lessons learned, the home secretary said in a Commons statement.
Her comments come as the Metropolitan Police revealed there are 600 counter-terror investigations active in the UK.
Armed police will be deployed at the football match between England and France at Wembley Stadium on Tuesday.
Prince William, who is president of the Football Association, has decided to attend the friendly out of "solidarity to the people of France", the BBC's Peter Hunt said.
Multiple attacks on bars, restaurants, a concert hall and the Stade de France on Friday left 129 people dead, including Briton Nick Alexander from Essex. The Islamic State group has said it was behind the killings.
A minute's silence was observed across Europe at 11:00 GMT on Monday, including at Trafalgar Square and the French Embassy in London, as well as in Northern Ireland, Scotland and Wales.
Among hundreds injured is Callum MacDonald, 24, from Fort William in Scotland, who was in the Bataclan concert hall where gunmen opened fire. He is understood to be in a medically-induced coma.
'They will fail'
Speaking in the Commons, Mrs May confirmed that new funding would be made available for an extra 1,900 security and intelligence officers at MI5, MI6 and GCHQ - an increase of 15%.
She said those who had attacked Paris "represent no-one and they will fail" to divide free countries such as Britain and France.
"France grieves but she does not grieve alone. People of all faiths, all nationalities and all backgrounds around the world are with you and together we will defeat them," she said.
The announcement on Monday that Britain's intelligence and security agencies are to be given a massive boost in resources has taken some there by surprise.
Expecting a modest boost in the coming Strategic Defence and Security Review, they have now been told they are to get a 15% increase in headcount, raising their numbers by 1,900.
For MI5, the Security Service and MI6, the Secret Intelligence Service, this will take some time to absorb, perhaps years. They will need to find, recruit, vet and train new intelligence officers largely from scratch.
But for GCHQ, the government's secret listening station in Cheltenham, it will be relatively easier for them to recruit already-qualified IT analysts and linguists from the commercial marketplace.
Deploying extra aviation security officers should also show results fairly quickly. They will be expected to assess security in overseas airports used by large numbers of Britons where security is suspected of being lax.
Mrs May said police and emergency services had been prepared for the possibility of a "marauding gun attack" in the UK since the 2008 Mumbai attacks, but plans would be reviewed in light of Friday's events.
"As soon as the attacks took place, we took steps to maintain the security of the UK," she said.
"The police have increased their presence on some streets and at some locations, and they will be intensifying their approach at events in big cities."
The UK's Border Force had intensified checks on people, goods and vehicles entering the UK - and was carrying out "targeted" security checks against passengers and vehicles travelling to France, the home secretary added.
She also said she would be lobbying her European counterparts for tighter gun laws across the European Union.
In other developments:
Number 10 says UK security services have disrupted seven attacks this year, including one in the last month
Funding for aviation security is to be increased, with specialist teams to look at key locations outside the UK
The Foreign Office is advising people travelling to France to exercise caution in public places and follow the advice of local authorities
Defence Secretary Michael Fallon says Britain must "think again" about military action in Syria - where IS operate - saying "France's fight is our fight"
Labour leader Jeremy Corbyn says he is "not happy" with UK security services operating a “shoot-to-kill” policy in the event of a terror attack
All 23 France players are travelling to England on Monday after turning down the option to withdraw from Tuesday's friendly at Wembley
England coach Roy Hodgson says the England v France match will not be a “normal friendly”
Mrs May said that in recent months, "a number of serious plots" had been disrupted in the UK, adding there could be "little doubt" that the threat posed by IS militants was evolving.
More than 750 people are thought to have travelled from the UK to Syria and Iraq, and approximately half of those have returned, she said.
The terror threat level in the UK has been at "severe" - meaning an attack is highly likely - since last August.
Earlier, UK Prime Minister David Cameron said world leaders had agreed to do more to share intelligence and cut off funding for terrorists, as the Paris attacks "underlined the threat we all face".
Speaking at the G20 summit in Turkey, he said the gap between Russia and the West's position on Syria "has been enormous", but now "everyone recognises the need for compromise".
Meanwhile in the UK, officers from the Met Police's Counter Terrorism Command unit are interviewing people returning from France who may have information.
The Met is also appealing for any potential witnesses to contact its anti-terrorist hotline, on 0800 789 321.