England have cut a swath through their Euro 2020 qualifying group, advancing to the finals on the back of free-scoring and expressive performances and, once again, they had too much for lowly ranked opponents.

It was a display of control from Gareth Southgate’s young team, which was marked by Harry Winks’s 32nd-minute goal – his first in an England shirt – and glossed by a late surge that showed how ruthless they can be when they find their connections.

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Harry Kane scored again. He always does. His poacher’s finish at the far post, following a cross from the recalled Raheem Sterling and a defensive slip from the Kosovo defender, Fidan Aliti, meant he has scored in all eight of the qualification ties. No England player has done that before.

The captain now has 20 goals for club and country this season – one in which he is supposed to be struggling.

Marcus Rashford, on as a substitute, scored the third with a cool first-time shot from Sterling’s second assist and there was time for another replacement, Mason Mount, to accept a ball from Kane following a glaring error by Ibrahim Dresevic and beat the goalkeeper, Arijanet Muric. For him, too, it was his first senior international goal.

The scoreline did not reflect a game that was tight for long spells but the manner in which England moved through the gears towards the end; how they put their opponents to the sword, bodes well for the finals. Rashford’s pace and directness was a potent weapon against a tiring Kosovo defence and one statistic stood out for the finals: England can reflect on a tally of 37 goals from the campaign, the most in Euro 2020 qualifying.

It has been a testing international break for Southgate, as he has dealt with the fall-out from Sterling’s bust-up with Joe Gomez, but, after last Thursday’s 7-0 drubbing of Montenegro at Wembley, this was another satisfactory outing. England are assured of being among the top seeds in the draw on Saturday week and Bernard Challandes, the Kosovo manager, described them as the best team in Europe because of their attacking potential.

England can rarely have been afforded a more loving welcome than the one they received here in Pristina – a legacy of the central role that Britain had played in forcing Serbia’s withdrawal of troops from Kosovo in 1999 and helping the nation towards its independence. The home fans held up St George’s crosses when the visiting anthem was played and the tie, which had been eagerly anticipated, stood as a symbol of solidarity, progress and optimism.

Facebook Twitter Pinterest Kosovo fans hold up England flags before the start of the match. Photograph: Steven Paston/PA

England wanted to embrace similar notions on the field and the positives that Southgate could take went beyond the lethal edge that his players showed in the final third. Winks caught the eye as a No8 rather than a midfield pivot, showing composure under pressure and linking to the forwards, while Ben Chilwell at left-back got his defensive angles right, showed assurance on the ball and motored up the flank.

Winks’s goal followed a nice bit of link-up play by Kane and a perfectly judged pass from Alex Oxlade-Chamberlain. Winks wrong-footed Dresevic with his burst forward and the only remaining question concerned whether he could finish when one-on-one against Muric. With a pause and then a shimmy, he outfoxed him and guided low into the near corner.

Kosovo knew they could not qualify via the group, although they might still do so through the play-offs, but it did not feel like a dead rubber. The host’s determination to impress England, their big brothers, saw to that. Challandes’ team have some technical players, although too often their final pass or action was loose. Nick Pope, on his first England start, was not extended in goal.

The slippery pitch did not help the players’ confidence and there were errors on both sides during a slow-burning first half, when Kosovo’s high press asked questions of England in possession. Southgate felt that Harry Maguire and Winks brought calmness when they set the play.

Facebook Twitter Pinterest Harry Kane scores England’s second goal to snuff out Kosovo’s hopes of a point in their final Group A match. Photograph: Michael Regan/Getty Images

It was not Callum Hudson-Odoi’s game, as he made a succession of loose passes in the first-half, but he did dart from left to right before shooting too close to Muric. England also threatened in the 15th minute after Chilwell’s run and cross and a Kane lay-off for Sterling. The winger’s shot drew a save from Muric.

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Kosovo flickered from a pair of corners at the start of the second half and it was a worry from an England point of view to see the space that Amir Rrahmani managed to find on both occasions. On the second his far-post header was wild.

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England had advertised the second goal. Kane hit the near post from Sterling’s pull-back after a Chilwell incision while Sterling was denied by Aliti’s saving challenge. Oxlade-Chamberlain sparked that move when he won the ball and found Kane and the Liverpool midfielder would hear praise from Southgate, who said he had shown his qualities in the No8 role. Yet Oxlade-Chamberlain looked distraught when he was substituted. Did he feel that the occasion had gone to his plan?

When Kane scored the second goal, it was the prompt for the grandstand finish and Southgate could also introduce Fikayo Tomori at right-back for his debut. England have tougher tests ahead. They will approach them with confidence.