It comes after footage online showed the far-right activist walking by a guy lying on the ground at the station shouting, “he come at me”.
Police were called to St Pancras on Monday (July 28) just after 8.40pm to reports of an assault.
A man was taken to hospital with serious injuries, which since are not thought to be life threatening.
Since then, police said that a suspect, a 42-year-old from Bedfordshire, boarded a flight out of the country.
Videos have been shared appearing to show Robinson boarding an airport shuttle in Tenerife.
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One video was captioned: “Spotted Tommy Robinson getting on my flight this morning.”
The British Transport Police has said it is looking to bring in the suspect who fled the country into custody for questioning.
In one video at St Pancras, a man who appears to be injured and laying face down on the floor was shown, with Robinson allegedly seen walking past.
After walking down, he returns back up and is heard shouting “he come at me”.
In another video, Robinson had also filmed himself that day while walking in the station.
A British Transport Police spokesperson said: “British Transport Police were called to St Pancras station just after 8.40pm on Monday (28 July) following reports of an assault.
“Officers attended and a man was taken to hospital with serious injuries, which are not thought to be life threatening.
“Overnight the investigation has been ongoing and officers have been making arrest enquiries.
“Officers have confirmed that the suspect, a 42-year-old man from Bedfordshire, boarded a flight out of the country in the early hours of this morning. Detectives are continuing to work closely to progress the investigation and bring him into custody for questioning.
“Anyone with information or who witnessed what happened can text 61016 quoting reference 655 of 28 July.”
