A man is currently being held in police custody in connection with the incident which happened near the Houses of Parliament shortly before 7.40am this morning.
It said officers would be stationed across England, Scotland and Wales, and were available to speak to anyone with concerns.
Superintendent Chris Horton said: “We know incidents such as this are likely to cause concern, so our officers will be highly visible both on board trains and at stations.
“We are there to reassure the travelling public so please don’t be alarmed if you see our officers, including firearms officers, on your journey.”
Also in crime: Violent crime on rise on Yorkshire's railwaysAnyone with concerns can contact BTP officers be sending a text to 61016 or by calling 0800 40 50 40.