Ordinarily there would be nothing unusual about a Conservative candidate holding a safe Conservative seat. But at a time of electoral volatility, Caroline Johnson’s comfortable victory in the Lincolnshire constituency of Sleaford and North Hykeham on Thursday is remarkable, mostly because of things that didn’t happen. The Tories might have been punished for incumbency, as often happens in byelections. Or they might have shed votes to Ukip in a region that voted strongly against European Union membership in June. In the event, neither thing happened.

The result – a Conservative majority of 13,144 and a 53.5% vote share – offers comfort to Theresa May after last week’s upset in Richmond Park, a seat where the balance of opinion on Brexit tilted the opposite way and the Liberal Democrats gained an MP against long odds. That contest was peculiar in many ways, not least the uncertain party status of the sitting MP, who defended a Tory majority while running notionally as an independent.

Sleaford was a more conventional race and Downing Street will see the outcome as a vindication of Mrs May’s approach to Brexit – signalling unambiguously that she intends to lead Britain out of the EU, while refusing to be drawn on detail. This frustrates her Westminster critics; but voters in Lincolnshire appear to give her the benefit of the doubt. Their verdict tallies with national polls that give the Tories a consistent and comfortable lead – up to 17 points in the latest poll. There is no sign yet of the kind of mass impatience or fear of backsliding towards Europe that would feed a Ukip surge.

There was a time when a mediocre second place would have counted as an achievement by Ukip, but expectations are higher now that the party’s defining mission has been ratified by referendum. A protracted shambles of a leadership contest has probably depressed the party’s vote, but the bigger problem is that Mrs May is seen as a safe custodian of the Brexit agenda among moderate leave supporters. Ukip’s Paul Nuttall could capitalise on their disillusionment if the government does something he can depict as a great betrayal. So far that accusation is not available.

By contrast, the Liberal Democrats have ample material for appeals to former remain supporters who feel scorned by the government. The Lib Dems were the only party to increase their vote share (albeit from a very low 2015 base) in Sleaford, rivalling Ukip for second place. There is some vindication here of Tim Farron’s approach to Brexit – choosing clarity over sophistication, pitching for the votes of anyone appalled by the turn events have taken since 23 June and desperate for uncomplicated resistance. It is clearly not a message for the whole country but a tactic to recover a sense of purpose and eke out a profile for a party that had lost both. Mr Farron’s plan appears to be working.

The same cannot be said of Jeremy Corbyn. There is no positive gloss to apply to Labour’s fourth place in Sleaford. Its vote share shrank seven points to 10% from 17% in 2015 (and 34% in 1997). This, too, is consistent with polls that tell a story of stagnation tipping towards decline. The simplest explanation for Labour’s dismal showing is that it has no coherent position on Brexit, which is the question of the moment and so bound to hover over the polling booth. But that reflects a deeper malaise. Mr Corbyn’s party struggles to express itself on Brexit because it is unsure of its instincts on matters that will define the UK’s post-EU status: border control, openness to global markets, willingness to project power through western alliances.

As a result, Labour offers a complaint about Conservative management but no alternative prospectus. There is nothing to instil confidence or hold together the coalition of the party’s traditional supporters that straddles divergent – arguably incompatible – attitudes on immigration and, by extension, Europe. These are deep structural problems – and they have built up over years. No leader could be expected to solve them overnight. But an essential measure of leadership, in the absence of ready solutions, is the ability to signal some interim strategy for recovery; some capability for reassurance that the quest for answers is under way; that the job, however difficult, is being done. It is the apparent lack of this remedial activity that is so profoundly damaging to Labour’s standing.

A pair of byelections in consecutive weeks shows Brexit is posing challenges to all party leaders. Polls reveal many voters uncertain where to turn. But it is only Mr Corbyn who appears to be salvaging no opportunities at all from this time of political turmoil.