British police have arrested a man on suspicion of assaulting a pensioner in a row over this week's referendum on whether Britain should remain in the European Union.

Police said the incident had occurred outside a department store in Carlisle, northern England, on Sunday morning.

"A 78-year-old man was struck in the face causing minor injuries by a 52-year-old man following an altercation about the EU referendum," Cumbria Police said in a statement.

The 52-year-old man was arrested shortly afterwards.

The debate between those wanting to leave the EU and those wanting to remain has become increasingly heated and febrile as the vote nears. Polls suggest the referendum, which will have huge implications for Britain, is on a knife edge.

Last week, Jo Cox, an opposition Labour lawmaker who supported staying in the bloc, was murdered in her constituency in northern England in what Labour Jeremy Corbyn told parliament on Monday appeared increasingly likely to have been a politically motivated attack.