Many former Labour voters who switched to the Conservatives at the last election in key electoral battlegrounds are showing no regret and little sign of returning to the fold, according to two prominent members of Jeremy Corbyn’s shadow cabinet.

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Gloria De Piero and Jonathan Ashworth, writing in the Observer, raise the alarm about the state of voter opinion after conducting a tour across parts of England where Labour has to recover if it is ever to return to power.

De Piero and Ashworth chose areas of England, outside the north, where the party was strong in the 1990s and remained so during 13 years of Labour government but has since fallen back, as the Tories have recovered and Ukip has emerged as a real force.

Over several weeks they conducted hundreds of conversations with voters and non-voters, trying to gauge why so many people had deserted Labour, how they viewed the party now, and what the party needs to do to win them back.

Despite Corbyn’s optimism that he can inspire a national movement behind his leftwing programme, the MPs found little evidence that ex-loyalists were thinking of returning to Labour.

Many – including some who voted Labour last year – were concerned about Corbyn’s opposition to renewing the Trident nuclear missile programme, and said they wanted a Labour party that puts strong national defence at the heart of its programme. “Our biggest challenge as a party remains convincing those who left us to consider us again,” they write. “We met many former Labour voters who had switched to David Cameron’s Conservatives, who – while not enthusiastic about the Tories – showed no sign of regret that they’d helped to elect a Conservative government.”

De Piero and Ashworth say they were “struck by the number of times concerns over defence were raised with us by Labour voters”.

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Many Corbyn supporters say that he will inspire the politically disengaged but the two MPs found no evidence for this either. “Sadly, we found those who don’t vote were as uninterested in politics as it is possible to be,” they write. “They had zero faith that there was anything any politician could do to change their lives. That is clearly the fault of politics, rather than those we spoke to, but the uncomfortable truth is that they are as determined not to vote as we are to try to persuade them to.”

After encountering “real hostility” to Labour from ex-supporters who have turned to Ukip, they say the party has to engage more actively with concerns about immigration.

Corbyn faces his biggest electoral test since becoming Labour leader in May, with elections in England and for the Scottish parliament and Welsh assembly, as well as that for a new mayor of London. His office is already playing down its chances in local elections across England and elections to the Scottish parliament but is confident that Labour’s candidate, Sadiq Khan, will defeat the Tory, Zac Goldsmith .