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Elsewhere, pro-Palestinian demonstrations prefaced Italy's vital win over Israel and Spain took another step towards qualification with a big victory against Bulgaria.
Thomas Tuchel's England brushed aside Latvia in Riga to make it six wins from six in Group K and guarantee top spot before their final two fixtures next month -- they have 18 points and an unassailable seven-point lead over second-placed Albania.
Anthony Gordon opened the scoring before Kane produced a lethal finish and then netted a penalty to make it 3-0 at half-time -- the Bayern Munich striker has 21 goals in 13 games this season for club and country.
Maksims Tonisevs scored an own-goal and Eberechi Eze added the fifth, with England now able to look forward to December's draw for next year's finals.
"It comes rarely that you qualify for a World Cup, so the mood is very, very good," said Tuchel.