Potesters who have been occupying the grounds of Government House, as well as the Makawan bridge leading to the complex, since April.
There was no claim of responsibility for the attack nor any immediate indication of who was behind it.
Police Captain Pompet Chotelang said all of the wounded were guards for the People's Alliance for Democracy (PAD), an opposition movement that has led the street demonstrations seeking to remove the present government.
"We can't confirm or deny the existence of any requests before an arrest is made"
Daniel Painter, British embassy spokesman
Another small explosive was thrown into the compound of a constitutional court judge earlier in theday, Pompet said.
It was not clear if that blast, which caused damage to the home but no injuries, was related to the ongoing political protests.
After Thursday's attack, the US embassy issued a warning urging citizens to avoid the area.
About 120 police officers holding shields stood guard outside the British and nearby Swiss embassies as hundreds of protesters waving flags and "Most Wanted" banners with pictures of Thaksin erected a steel barricade and sealed off the main road.
"Why doesn't England send Thaksin back to Thailand to be put in jail?" Sarocha Pornudomsak, a PAD spokeswoman, shouted to the crowd.
"We are here to tell [British Prime Minister] Gordon Brown that England should not keep a bad guy in the country."
Daniel Painter, a spokesman for the British embassy in Bangkok, said he was unable to comment on Thaksin's status or whether extradition proceedings were under way.
"We can't confirm or deny the existence of any requests before an arrest is made."
In August, Thaksin fled to Britain claiming he will not get a fair trial in Thailand on the corruption charges that have mounted against him since his overthrow in a September 2006 coup.
Protesters accuse Thaksin of corruption and Somchai Wongsawat, his brother-in-law and the current prime minister, of being his proxy.
Somchai has been forced to operate out of a makeshift office at Bangkok's old international airport after PAD protesters vowed not to leave the prime minister's compound until all of Thaksin's allies were out of power.