Is the power of the Labour left on the wane? That’s the conclusion some have rushed to in the aftermath of the party’s candidate selection for next month’s by-election in Lewisham East.

The comfortable victory of Janet Daby, Lewisham’s deputy mayor, over Sakina Sheikh and Claudia Webbe, who were backed by Momentum and Unite respectively, has prompted declarations of victory for the Corbynsceptic cause.

That it has been cast as such betrays the inability of lots of people to think about Labour in anything but primary colours. Though Daby was endorsed by Progress and Labour First, it doesn’t follow that she is ideologically as one with either group. Her having voted for Corbyn twice proves that much.

It might not prove much else beyond that, but it underlines just how limply Labour selections have come to be analysed: Daby might not have been backed by the left but she did not, unlike Labour candidates in last year’s by-elections in Copeland and Stoke, run as a Corbyn critic and instead wore her personal allegiance to his leadership heavily.

The left’s preferred candidates might not win every selection, but more and more of those who win in their stead are supportive of the leadership by default.

The one respect in which this is not true in Daby’s case is on Brexit: she campaigned on a platform of keeping Britain in the customs union and single market, a stance aligned with that of most Corbynsceptic MPs. Neither Webbe nor Sheikh promised outright to defy the whip as Daby did.

Her victory in this limited respect is annoying for the leadership, insofar as it shifts the conversation back onto uneasy Brexit turf, which neither Barry Gardiner nor Len McCluskey appeared particularly comfortable on this morning, and highlights the gulf between large sections of the membership and the official party line on that particular issue. But, as Stephen wrote last week, the rebels on Brexit Labour has to worry about are those representing Leave constituencies, whose hostility to a Norway-style EEA deal would likely outweigh any Tory rebellion. Replacing Heidi Alexander like-for-like on Brexit does not change this dynamic. Daby herself also undermines a simplistic pro-EU equals Corbynsceptic reading.

Outside of the PLP, Daby’s selection offers further consolation for the left. Had Claudia Webbe been selected, she would have been removed from the party’s ruling national executive committee in favour of Bex Bailey, a Corbynsceptic. The resignation of Christine Shawcroft in March let Eddie Izzard, another Corbynsceptic, on to the NEC, and while the left has a comfortable majority, ceding a second seat by attrition would only have caveated their success in winning the selection.

Though the narrative that Labour’s left is weaker than it looks got another outing yesterday, there is little evidence in Lewisham to suggest it is anything more than wishful cliche.