Immigration can be a euphemism for race, and Labour should not be afraid to fundamentally change the conversation about the benefits of migration, the shadow home secretary, Diane Abbott, has said.

In a speech where Abbott pledged Labour would end family break-up through the immigration system, the MP said the party’s immigration policy in government would be value-led and humane.

Abbott said the success of Labour in the 2017 general election, against the grain of its sister centre-left parties in Europe, showed it was possible to win votes without scapegoating migrants.

“You will have noticed the absence of immigration control mugs,” she said, in reference to the “Controls on Immigration” mugs in Ed Miliband’s 2015 campaign.

Abbott, the first black woman to win a seat in the House of Commons, said she remembered Enoch Powell’s “rivers of blood” speech as a schoolgirl 50 years ago.

“I remember Enoch Powell’s speech, I think I was in primary school, and I wasn’t following it in huge detail, but I do remember how I felt,” she said, giving a lecture at King’s College London’s Policy Institute. “People were talking about it even in school and I felt frightened. I didn’t quite know why, I didn’t know exactly what had been said, but I felt frightened.

“And of course, one of the issues around immigration in some political quarters is that immigration is a euphemism for race, and you can’t have a serious debate around immigration unless you are prepared to face up to that.”

Abbott said Labour would provide more details on how a post-Brexit immigration system would work in the coming months, but said there would be no target, and jobs and the economy would be prioritised.

“We need a values-based approach to immigration. I am confident, in the coming months, we will be setting out immigration policies that meet the test of being firmly located in Labour’s values,” she said.

Abbott has previously been a firm supporter of free movement within the EU, which has sometimes put her at odds with shadow cabinet colleagues. But she has said she is not in favour of preferential treatment for EU citizens versus non-EU citizens for a future migration system.

However, she said Labour would not put curbs on immigration ahead of economic considerations when negotiating a Brexit deal.

“In trade negotiations, our policy favours growth, jobs and prosperity. We make no apology for putting these aims above bogus immigration targets, we mean it,” she said.

“We will do nothing that harms the prosperity of the majority of people in this country. We will certainly do nothing which hurts jobs, which is relevant in the current debates we are having about the single market and the customs union.

“Immigration is subordinate to our priorities which favour growth, jobs and prosperity.”

The party “has never had an open door policy”, Abbott said, pledging the party would recruit 1,000 more border guards to tackle illegal immigration and people trafficking.

She said Labour would extend the same rights to EU citizens who arrived in the UK during the transition period as those who were in the UK before Brexit, which Theresa May has said she will oppose.

“We don’t want a two-tier system for EU nationals, and apart from anything else, it would lead to a complexity that I doubt the immigration services could actually handle,” Abbott said.

The new commitment to ending family break-up in the immigration system would allow the carers or parents of admitted child refugees to come to the UK, Abbott said. Labour would also end the practice of deporting children without entitlement to be in the UK once they turn 18, even when their parents have leave to remain.