A Champions Cup of modest returns for the English was at least given a fillip by Harlequins. This reasonably comfortable win over Glasgow across the road from where the Calcutta Cup will be contested next month put the home team through to the last 16. No one will particularly relish a visit from one of the game’s more waspish teams, but it is fair to say any further progress by Quins will require an improvement on this.

Glasgow, champions of the United Rugby Championship no less, were not quite there all evening. Perhaps they were thrown by the loss of Sione Tuipulotu to a suspected pectoral injury this week in training, which threatens his participation in Scotland’s Six Nations campaign. Franco Smith, Glasgow’s head coach, could not confirm the extent of the injury but spoke darkly about Tuipulotu’s prospects of an immediate return, implying afterwards that the race was more for him to return in time to mount a challenge for a place in the Lions tour than the Six Nations.

Glasgow did score an absolute beauty in the first half but they could not rouse themselves to score again. Their qualification was already assured, complete with home tie, but this was a disappointing end to their pool.

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Quins failed to secure the bonus point, which might have proved significant, but Racing’s win over Stormers means only Sale can pass them in third. The Sharks host Toulon, now confirmed winners of Pool 4, in Manchester on Sunday . A bonus-point win for Sale would push Quins into fourth, still enough for a place in the last 16.

Tuipulotu was not going to play in this game anyway, but the news for Gregor Townsend worsened only 10 minutes in when Scott Cummings, one of Scotland’s locks, was forced off. He later appeared with his arm in a sling.

Better news was forthcoming in the form of Tuipulotu’s replacement, Stafford McDowall, who also assumed the captaincy in the absence of Kyle Steyn. He was instrumental in that Glasgow try on the half-hour.

McDowall’s pass released Kyle Rowe down the left wing, straight from a scrum in Glasgow’s own half. He kept up in support to take the return ball and slip it to Jamie Dobie, whose offload sent Tom Jordan to the posts.

That was a highlight in a first half full of them, before the game drifted in a flatter second. Quins had already opened a 17-0 lead at that point with two tries in the first quarter and a Marcus Smith penalty. Cadan Murley, included in Steve Borthwick’s England squad, was key to both tries, before clinching Quins’ third in the final quarter.

He took Smith’s cross-kick in the 14th minute and set up position deep in Glasgow’s right corner. Two meaty drives by Quins’ locks paved the way for Chandler Cunningham-South, looking good again on the eve of the Six Nations, to open the scoring.

James Chisholm was one of those locks, moved up from his customary role in the back row, and he weighed in with the second. Murley came in from the blindside off an attacking Quins scrum to release Nick David on a run down the right. Cunningham-South’s offload sent Chisholm off on a gallop to the line. Another Murley run coaxed Glasgow into an offside position, and Smith opened up that 17-0 lead with the penalty.

Quins thought they had a third just before the break, when the punchy Ben Waghorn dummied and went, but the television match official alerted the referee to an obstruction. Oscar Beard’s dummy had opened up the gap for Waghorn by obstructing Huw Jones.

A 10-point lead at half-time was better than nothing, but Quins respected Glasgow enough not to feel comfortable with that. The Warriors did go on to dominate the third quarter. It was Quins, though, who took the only bold step of the second half, as deep into it as the 68th minute. Glasgow were on the attack, but the home team turned the ball over, and Alex Dombrandt released Murley down the left. No one was at home for Glasgow. Murley put down his latest marker to Borthwick by running to the posts.

By then, the bonus point mattered not to Quins’ qualification chances, thanks to the result in Paris. Quins were not to know that, though, given the concurrent kick-off. They finished the match in the ascendancy, but a fourth try proved beyond them. Still, a fourth team through to the last 16 is of some consolation to English rugby.