Mr Samak was initially praised for his restraint in dealing with the protests
British citizens in Thailand should avoid large gatherings and stay away from airports hit by demonstrations there, the Foreign Office has advised.
Thousands of anti-government protesters have occupied government offices in Bangkok and closed airports in the holiday areas of Phuket and Krabi.
The Foreign Office said people were not being told to stay away altogether but to regularly check their travel advice.
It said it did not know how many Britons could be affected.
A spokeswoman said: "We are advising British citizens to exercise caution, avoiding areas with demonstrations or large gatherings of people."
Britons planning to travel to or from the affected airports were advised to contact their travel operator.
The spokeswoman said the Foreign Office had been contacted by Britons in Thailand, but had no way of estimating how many may be stranded there.
In 2007, some 860,000 Britons travelled to Thailand
A spokesman from the Association of British Travel Agents (Abta) said the majority of British holiday makers travelling to Thailand fly into Bangkok airport, which remains open.
He said tour operators had been organising alternative travel arrangements - such as charter buses - to take people to and from the areas with closed airports.
But he also said independent travellers may find difficulty in booking last-minute overland alternatives to their flights.
The FCO website said rail services in north, north-east and southern Thailand are currently suspended.
The Abta spokesman added that it would be the responsibility of the airline to put anyone who had missed their plane through no fault of their own onto a later flight.
Claudine Pearson from Edinburgh told the BBC earlier that she thought it unlikely she would be able to catch her flight from Bangkok.
She said: "I'm currently stuck in Krabi, southern Thailand. I have a flight out of Bangkok tonight but as the airport and now rail links have been taken over by the PAD [protest group People's Alliance for Democracy] - it seems unlikely I will be able to catch the flight.
"I at no time felt threatened or uneasy and the protesters actually apologised for the inconvenience.
"It was very eerie, though, to see a busy airport reduced to an empty building with no planes in sight," she added.
Nik Wright told BBC News he and his wife who are in Thailand on their honeymoon, along with their four children, had been stranded in Phuket for two days.
He said: "I am due to start a new job on Tuesday, my eldest daughter is due to start senior school on Tuesday and my youngest daughter is due to start infants' school on the same day.
"Will we be home in time? I really do not know, no-one seems to know."
Sept 2006: Bloodless coup by military sees PM Thaksin Shinawatra removed from office
April 2007: New military-drafted constitution approved
Dec 2007: General election won by People Power Party (PPP), seen as reincarnation of Thaksin's now banned Thai Rak Thai party
Jan 2008: Samak Sundaravej chosen as PM
Feb 2008: Thaksin returns from exile
May 2008: PAD protests against Samak begin
July 2008: Thaksin goes on trial for corruption; his wife is found guilty of fraud. By mid-August the family has fled to the UK
August 2008: PAD protests escalate
Thai Prime Minister Samak Sundaravej has come under intense pressure to resign by protesters who accuse his government of being a front for the exiled former Prime Minister, Thaksin Shinawatra.
But despite the mounting pressure, Mr Samak has refused to step down from office.
Conservative group the PAD is leading the protests against Mr Samak's government.
On Tuesday, thousands of PAD supporters took to the streets of Bangkok and forced their way into government buildings.
Mr Samak was initially praised for his restraint in dealing with the protests, but he suddenly found his position weakened on Friday when the police pulled back and the triumphant protest leaders were left in control of the government complex.
About 2,000 protesters then besieged the city's police headquarters, prompting the police to fire what appeared to be tear gas to disperse them.
The PAD was originally formed in the months before a 2006 military coup which ousted Mr Thaksin. It has re-emerged now that the country is being led by his former ally Mr Samak.