Police were heard to tell anti-Thatcher protesters in Trafalgar Square that Millwall football fans had joined the demonstration and were "throwing bottles of urine" at officers.
Millwall supporters were earlier involved in crowd trouble during the club's FA Cup semi-final against Wigan at Wembley.
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The Prime Minister has praised the former soldier's "huge professionalism" in trying to save the life of Pc Keith Palmer.
The man who carried out the Westminster attack is thought to be British born and was once investigated by MI5, the Prime Minister has said.
Jason Day, who lost his father to stomach cancer at the age of 12, broke down in tears as he explained his shock exit during the WGC event.