There have been almost 100 acts of violence, harassment and vandalism against Muslims and mosques since last Thursday's attacks, police said.
Some of the incidents took place in Scotland, with a reported racist assault in Edinburgh and graffiti being daubed at a mosque in the city.
Rob Beckley, the Association of Chief Police Officers' spokesman on community tension issues, yesterday said there did not appear to be a concerted campaign of revenge attacks.
However, he said there had been a number of incidents where Muslims or people of Asian appearance had been targeted for abuse or assault.
He said officers were stepping up patrols and working with a variety of community groups in an effort to provide reassurance, and promised that police would respond "robustly" to any race or faith hate crimes.
"Since last Thursday there have been things like criminal damage, some minor assaults, abuse in the streets and e-mail abuse," he said.
"We're not seeing hundreds, nevertheless the fear and the impact of all these individual incidents is very high. So we're trying to ensure that we respond very robustly to any incidents that we learn about.
"They are not all directed against Muslims, some have been directed against people of an Asian appearance. The fear is very palpable - that is what we have to acknowledge and respond to."
In Leeds, Zaher Birawi, the chairman of the city's Grand Mosque, expressed anger and sadness that bombers appeared to have come from the city.
"It is nothing to do with Islam at all. The main concern in the community now is what will happen next, what is the reaction of the community," he said.
In Edinburgh, police were yesterday investigating an unprovoked racial attack on two Asian boys. The 16-year-old and his 11-year-old friend were assaulted by a white man on Tuesday afternoon.
They were walking down Leith Walk near Lorne Street when the attacker punched the older boy to the ground, causing him to knock his head on the pavement. The man is believed to have hurled racial abuse at the youngsters before making off towards Leith.
There was further evidence that Edinburgh's Muslim community is being victimised at a mosque and a community centre. The buildings have been defaced with messages including "Islam Scum" and "This centre sympathises with terrorists".
The graffiti attacks happened at the Sha Jalal Mosque in Annandale Street Lane, and the Pakistan Community and Cultural Centre in Annandale Street at the weekend.
Superintendent George Simpson, of Lothian and Borders Police, said: "These incidents are appalling and there is no space for this behaviour in the democratic society we live in."
In Norwich, two women were released on bail after a mosque was vandalised in a racist attack.
The attack in Rose Lane, in Norwich city centre, came after religious and political leaders across the world urged the public not to link last week's blasts in London with the wider Muslim community.
Police said two women had been arrested and released on bail in connection with the vandalism at the Islamic Centre in central Norwich. Four windows were damaged in the attack, which took place at about 3am on Sunday.
And in Nottingham, a 16-year-old charged with the manslaughter of a man who died following an alleged racist attack was due to appear in court yesterday.
Kamal Raza Butt, 48, who was staying with friends in Nottingham, was found collapsed on Sunday afternoon and died before reaching hospital.
Ken Livingstone, the London mayor, yesterday urged people not to judge Muslims on the basis of the attacks.
He said: "We don't judge Christianity by the two or three mass murderers there were in Serbia. We shouldn't judge this great faith by a handful of fanatics."
He added: "You don't judge one of the great world religions, which has been behind so much progress in human history, and is overwhelmingly dominated by people who look for peaceful co-operation, by a handful of fanatics."