The Foreign & Commonwealth Office (FCO) advises against all but essential travel to Bangkok and specific parts of Thailand.
It advises travellers to "be aware that acts of violence or sabotage might be staged outside the Red Shirt protest area".
A statement on the FCO website said: "A threat has been made by the Red Shirts to set off explosions in department stores in Bangkok. Although no such incidents have occurred outside the cordon since it was imposed by the military, the potential risk can not be ignored."
"If you are already in Thailand, we advise against all but essential travel to Bangkok. Wherever possible, you should take transport services that do not involve transiting areas of Bangkok where political protests are taking place."