"There is a high threat from terrorism. Further attacks targeting westerners may occur," the British government said in its summarised travel advice.
It said the attacks on western nationals in Bangladesh could be "indiscriminate" in nature and asked Britons to "be particularly vigilant, consider your movements carefully and take appropriate security precautions."
A UK High Commission spokeswoman in Dhaka, however, said the new travel alert did not ask British nationals to not visit all parts of Bangladesh.
The new British alert came two days after foreign diplomats demanded extra security measures for their nationals in the country in a meeting with senior government leaders at the foreign office here.
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The diplomats were reassured that highest security will be provided to foreigners living in Bangladesh.
"We talked about additional security measures everywhere," British High Commissioner in Dhaka Robert Gibson told reporters after the meeting.
The ISIS had also claimed responsibility for both the killings.
However, the government says it did not find any link of the murders with the terror group. The US has offered Dhaka its assistance to fight the Syria-based Islamist group.
Prime Minister Sheikh Hasina has also ruled out the possibility of Islamic State involvement in the murders, blaming the Opposition BNP-Jamaat alliance for the killings.
"Bangladesh has a Prime Minister who has taken a zero tolerance approach to terrorism (and) we have everything we need to fight the emergence of IS in Bangladesh," she said.