The UK Foreign Office has advised against all but essential travel to several Egyptian cities as anti-government protests continue.
It warned against travel to Cairo, Alexandria, Suez and Luxor as Foreign Secretary William Hague spoke of his deep concern at the levels of violence.
About 30,000 British tourists are in Egypt, mostly at unaffected Red Sea resorts.
Meanwhile a noisy demonstration was held at Egypt's embassy in London.
The Foreign and Commonwealth Office (FCO) said an evacuation was not being considered yet and told Britons to observe the curfew.
Violence has flared on Egypt's streets for five consecutive days now as protesters clash with security forces, despite a curfew and President Hosni Mubarak's promise to appoint a new cabinet.
Mr Hague said in a statement: "We call on the government to exercise restraint and on the Egyptian people to pursue their legitimate grievances peacefully.
"President Mubarak spoke last night of his commitment to take new steps towards greater democracy and freedom for the citizens. We call on him now to listen urgently to the aspirations expressed by the Egyptian people.
"He must seize this moment to make these reforms real and visible and to base them on the universal values that are the right of people in all countries."
He added that the situation in the Red Sea resorts remained calm and said the Foreign Office was in regular contact with travel operators and extra consular staff were in Cairo to help British nationals.
Shadow foreign secretary Douglas Alexander said this was "the moment where Egypt can move from protest to progress".
He said political, social and economic reform was needed, but violence must be avoided.
More than a million UK citizens visit Egypt annually but the majority head to Red Sea resorts including Sharm El Sheikh and Hurghada - an eight-hour drive from Cairo.
The Foreign Office altered its travel advice for Egypt on Friday, and stressed that the warning in place for Cairo also extended to Giza, a suburb of the capital where Egypt's most famous Pyramids and Sphinx are located.
The Nile-side city of Luxor is also affected by the advice, as it is popular with British tourists visiting its array of ancient Egyptian artefacts and ruins.
Flights are being cancelled and rescheduled to avoid travelling during the curfew and operators are cancelling excursions to the Egyptian capital.
- All BMI flights between Heathrow and Cairo on Sunday have been cancelled, with passengers given the option to rebook.
- On Saturday, the airline's flight BD771 was turned around and returned to Heathrow "due to the rapidly-changing situation" and flight BD772 scheduled for Saturday evening was also cancelled.
- Thomas Cook said it had scrapped all excursions to Cairo this weekend from the Red Sea resorts, but its flights were operating in and out of Sharm El Sheikh airport as normal.
- Thomson and First Choice said they were not operating any excursions into Cairo and were monitoring the situation.
- The military has closed tourist access to the Pyramids, according to the Associated Press news agency.
- British Airways said it had changed the times of Cairo flights to operate outside the curfew and was offering passengers the option of changing the date of travel, getting a refund or travelling to another destination.
- BA has chartered a plane to bring home up to 90 people who want to leave Egypt. The flight is expected to land at Gatwick at 2100 GMT on Saturday.
- Abta, the organisation formerly known as the Association of British Travel Agents, said it had not heard of any reports of British package tourists being affected by the unrest.
Foreign Office Minister Alistair Burt said Britons should avoid crowds and demonstrations, observe the curfew and monitor the Foreign Office website for updates.
Meanwhile, an EgyptAir flight from London Heathrow to Cairo was diverted to Athens after a note containing the word "bomb" was apparently found on board.
The Foreign Office said consular staff in the Greek capital had made the 50 British passengers aware of the latest travel advice. The passengers stayed in Athens overnight.
In London, several hundred people gathered outside the Egyptian embassy to show solidarity with the protest against President Mubarak's 30-year rule.
BBC correspondent Ben Ando, who was at the scene, described the rally as "noisy but contained".
One unnamed campaigner, a 29-year-old doctor from London, said: "It is time for change. I think President Mubarak will go - I think he will have no choice.
"I have family in Egypt and they are seeing the protest and disruption. I think so far life is stable. My worry is after this, it won't be."
Other demonstrators, from the radical Muslim group Hizb-ut-Tahrir, gathered nearby, chanting "go, Mubarak go".
Fears of violence
Their banners called for khilafah, or the Islamic way of life, saying "Arab puppet rulers must go" and "Arab-Muslim rulers are traitors".
The protesters' numbers were swollen by a number of demonstrators carrying placards against higher tuition fees, who had been involved in a separate demonstration in the capital.
As more arrived around the embassy at around 1600 GMT, some of the organisers of the Egyptian protest left, voicing fears events could turn violent.
One said: "We will see how things go and, if they don't change, we will be back here next Saturday."