Police in Britain are urging people to be even more vigilant, after the blasts in Istanbul which killed at least 27.
Concrete blocks prevent suicide car bombers getting at Parliament
The two suicide bombs were directed at UK targets, including the British consulate and the London-based HSBC bank. At least four Britons died.
Security officials in the UK have been on their second highest state of alert for several days, after intelligence of another attack planned for the UK.
Police urged the public to be alert and tell them about anything suspicious.
Britain also said it had new information which led it to believe further terror attacks
may be attempted in Turkey.
A Foreign Office spokesman said he could not give
details, but that the government had tightened its travel advice to Britons, warning them to stay away from major Turkish cities.
The security services within Britain believe they are currently dealing with two different cells of terrorists.
The UK is officially on high alert, but within this is a tier of internal and usually secret levels - which have gone from substantial to severe general
One is of North African origin, as yet untraced, and is thought to be planning an attack in the UK.
Security officials raised their alert level to six out of a possible seven at the weekend, after intelligence about this group.
They believe a different group carried out Thursday's attacks in Turkey.
On Thursday afternoon the Home Secretary David Blunkett met security chiefs who are investigating whether al-Qaeda sympathisers in the UK had been in touch with the bombers in Turkey.
They are also trying to establish why there was no intelligence warning of the threat in Turkey.
"We believe that the network, whilst loose, is very closely in touch and what is happening in one place obviously has a major knock-on on the other," Mr Blunkett told BBC News.
"Which is why we ask people to be vigilant, it's why we've taken the steps we have".
But shadow homeland security minister Patrick Mercer accused Labour of being "numbingly
complacent" about the threat to Britain and British interests.
"If the government has not realised how lucky Britain has been so far, these
attacks have not succeeded until today, then I hope they will be fully aware of
just how dangerous the threat to our homeland security is.
"The government must start to act much more positively; it must start to issue warnings to the public in Britain when the threat is high and it must
start to take sensible measures in order to protect people in this country.
"For instance there were failed attacks against both British and American diplomatic premises earlier this year.
"America has moved her consulate to a less
vulnerable position and has made it almost bombproof: Britain has not. Why not?"
Britain's leading police officer, Metropolitan Police commissioner Sir John Stevens, has sent 16 anti-terrorist officers to Istanbul to assist with sifting evidence which could identify the bombers.
He said security in the UK was not being increased because the state of alert was already at the highest it could be.
Warning UK residents to be alert but not frightened, he said: "We are making sure that security is maintained at its highest.
"We increased security three or four days ago after receiving reports saying
we needed to do that.
"We are at the highest level of alert in the country and we can go no further.
"Do not be alarmed, be alert, if there is anything suspicious get in contact with police."
BBC security correspondent Frank Gardner said the attacks in Turkey bore all the hallmarks of al-Qaeda.
Warning to Britain
"They were suicidal, they used truck bombs and high explosives... they were very finely co-ordinated, they attacked Western interests.
"And interestingly, as with almost all the big hits by al-Qaeda, they didn't give a stuff about killing civilians from the local community who happened to be in the way.
"Furthermore, about a month ago Osama Bin Laden issued a warning threatening retaliation against all the nations that are taking part in Iraq.
"Top of the list was Britain," he said.
Earlier in the day, Prime Minister Tony Blair said Britain would not "flinch" from its war on terror because of such attacks.
Mr Blair rejected any suggestion the UK and United States brought such attacks on themselves, saying "America did not attack al-Qaeda on 11 September, al-Qaeda attacked America".