Both countries updated their travel advisories for South Africa Monday.
It follows a warning by the US government over the weekend.
US embassies said it had received information that terrorists were planning attacks on places frequented by foreigners visiting Johannesburg and Cape Town, such as shopping malls.
The British embassy in Pretoria says the revised advisory should not be seen as a terror alert.
Earlier, the ministry of State Security, confirmed that they view the US government's warning in a serious light.
The department added that terrorism is a concern globally.
Meanwhile South Africans are unsure of weather or not to take the United States terror alert seriously.
We spoke to the Director of the Afro Middle East Centre, Na'eem Jeenah.