Labour spokesman called the video "alarming & unacceptable."
"We have confidence in the Ministry of Defence to investigate & act on this incident," the spokesman said.
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British MPs condemned "this type of behaviour," especially in the light of heightened political tension in the UK due to Brexit uncertainty.
Members of public also took to social networks to express their views on the incident.
Earlier this year, British MPs have appealed to police forces to take measures after cases of verbal clashes between Brexit protesters and the politicians occurred outside Westminster.
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"This behaviour is totally unacceptable and falls well below the high standards the Army expects," an Army spokesperson, quoted by British media, said.
The practice is understood to take have taken place at New Kabul Compound in Afghanistan and are part of 3rd Battalion Parachute Regiment.