The far-right activist Tommy Robinson has arrived in Tenerife as British police seek to question him over an alleged assault after he was filmed close to a man who was left seriously injured on the ground.

Robinson flew to Spain from the UK early on Tuesday. On Monday evening video emerged of him saying “he come at me”, an apparent claim of self-defence, at the scene of the alleged assault in St Pancras station in London as a 64-year-old man lay motionless on the ground.

The injured man was still in hospital on Wednesday in a stable condition. Police are understood to be treating him as a victim, not a suspect, at this stage. Police have said he was admitted to hospital “with serious injuries which are not thought to be life-threatening”.

CCTV from the busy central London station has been recovered and is being studied by detectives.

British Transport Police (BTP) say they were called to St Pancras at about 8.40pm on Monday to reports of an assault. A source said detectives were confident they had identified the suspect for the alleged assault and were not seeking anyone else.

Police are understood to have several lines of inquiry, one of which is locating Robinson. While he is known to have arrived in Tenerife, in the past he has travelled around Spain and into Portugal and Cyprus, sometimes relying on the hospitality of wealthy friends.

Robinson, whose real name is Stephen Yaxley-Lennon, is a former leader of the extreme-right English Defence League. The far-right monitoring group Hope Not Hate describes him as the “best-known far-right extremist in Britain”.

Police believe Robinson, 42, originally from Bedfordshire, took a flight out of Britain shortly after a video was put online showing him near the injured man.

The video shows Robinson claiming the man had attacked him first, and was filmed at St Pancras station, where he had been leafleting earlier in the day.

BTP said on Tuesday: “Following a report of an assault at St Pancras station last night (28 July), 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.”

In the video, a man can be seen lying face down and motionless, with Robinson pacing nearby. Robinson can be heard saying: “He come at me bruv.” Shortly afterwards, Robinson tells an onlooker: “He come at me, you saw that.”

The video seen on social media does not show how the injured man came to be lying motionless on the floor.

Nothing known publicly at this stage proves or disproves any version of the alleged assault, nor who may have been at fault.

The Conservatives’ home affairs spokesperson, Chris Philp, a policing minister in the last government, told the Guardian that the case raised questions about border security.

Philp said: “The fact that a wanted fugitive was able to pass through our international border should not be allowed to happen and it is further evidence of this government’s complete lack of border control, inbound or outbound.”

A government spokesperson said: “This is an operational matter for the police.”