Labour will seek to beef up its pitch to voters on immigration with a pledge to pay for 1,000 extra border guards by imposing a charge on visitors from the US and 55 other countries.

Yvette Cooper, shadow home secretary, will criticise other parties for engaging in an “arms race of rhetoric” on the issue, which has been thrust to the centre of political debate by the rise of Ukip.

But she will accept that the opposition “needs to talk more” about public concerns and will say action to restore public confidence that illegal entrants are being caught and dealt with is “vital for a progressive approach”.

Under the proposals, nationals in countries enjoying a “visa waiver” system of fast-track permission to enter the UK will be hit with a charge of around £10 per visit, which the party said would more than cover the £45m cost of the additional staff.

That is a similar sum as the US charges for its equivalent service and Labour said tourism experts did not anticipate it would have any impact on the numbers choosing to travel to Britain.

Regular increases in the cost of general visas since 2010 – from £68 to £83 – had not resulted in reduced visitor numbers from countries not benefiting from waiver arrangements, aides said.

As many as 5.5m travellers a year will be subject to the new fee – more than two in five of those from America, with Australians and Canadians the next largest groups.

“Enforcement has got worse in the last five years,” Cooper will say in a speech.

“Under (home secretary) Theresa May, basic checks are just not being done, and that is undermining confidence in the whole system.

“The number of people stopped and turned away at the border has halved. A smaller proportion of people absconding at the border are being found. And we recently discovered 175,000 failed asylum seekers may not be removed because the department has ‘limited resources’.”

She will point to a “serious and growing problem” of immigrants taking increasingly desperate steps to get to the UK from Calais, including “awful cases of young men camping by the roadside then leaping onto the wheel arches of passing lorries, only to be crushed and killed”.

Addressing the wider issue, she will say: “Too often the debate about immigration becomes polarised and unhealthy.

“On the one hand we now have an arms race of rhetoric involving the Tories and Ukip over immigration. Ukip are exploiting peoples’ fears, fuelling anxiety and division, and David Cameron is racing to catch up.

“On the other hand some people seem to think talking about immigration at all is a problem and they dismiss people’s genuine concerns.

“Both sides shout at each other. Neither are right. And most people don’t agree with either of them.

“In a shouting match, sensible voices are sometimes not heard. That’s why Labour needs to set out practical reforms as part of a sensible debate on the changes we need.”

Labour wants to convert all visa waiver arrangements to the electronic version introduced this year for passport holders from the United Arab Emirates, Qatar and Oman for visa-free stays of up to six months.

May said Labour’s proposed charge would apply to only around 230,300 people, and could pay for only 59 border staff.

“Even before Yvette Cooper’s speech, this announcement has unravelled completely,” she said.

“Labour are pretending they can hire 1,000 more immigration staff when their funding model would raise enough money for only 59 new staff members. And as their secret spending review contains plans to cut the Home Office budget, they are being especially dishonest.

“And what’s more, by relaxing the government’s immigration reforms, Labour would take Britain backwards and risk a surge in both legal and illegal immigration.

“This disastrous policy launch shows Labour aren’t remotely ready for the responsibility of government.”