“Take back control” drove the Brexit vote, and Theresa May is alarmingly clear: immigration control comes first – even if leaving the single market devastates the economy. But with the existing border control system under extreme stress, checks or visas for 100 million EU arrivals each year will mean a vast increase in workload for a Border Force that is already overstretched. Here’s just one practical reality that makes Brexit look more shocking by the day.

May missed all her targets when she was in charge of immigration as home secretary, so she knows better than anyone the impossibility of cutting net migration down to “tens of thousands”. She knows UK border controls are inadequate: police find 10,000 people each year who have entered ports in the backs of lorries, and Dover’s Tory MP Charlie Elphicke claims many more, never detected, step straight into the arms of traffickers.

Public sector cuts have not spared the service that is supposed to security-check all arrivals at a time of a raised terror threat. The new home secretary, Amber Rudd, went to Heathrow in July to see how her Border Force performs. She might have expected our biggest port to be the best run, and on her visit she saw all the desks fully manned, with minimal queues at passport control and plenty of smiles.

What she probably wasn’t told was how many of those desks were staffed by people pulled in from everywhere else, including HMRC tax officers from Newcastle, who were put up in hotels. (Can HMRC spare them, when they are only checking 4% of self-assessment tax forms?)

Had she asked staff about their workloads, they probably wouldn’t have told the truth, governed as they are by a regime of terror and targets. I spoke to some Border Force staff, on condition of strictest anonymity, meeting them miles away from Heathrow for fear of disciplinary action if they were caught talking to a journalist. With no culture of transparency, this service punishes whistleblowers.

Here’s what they told me: after the public row over gigantic queues before the 2012 Olympics, strict targets were set: non-EU passengers must queue for no more than 45 minutes, EU for 25 minutes, and fast-track first class just 15 minutes. These targets must be met 95% of the time.

At present, they are met 70% of the time, and staff shortages mean that civil servants brought in from elsewhere get just a few days’ training. “All they can do is a basic passport scan,” say these whistleblowers. “Training and experience matter. We can feel whether something is wrong about who they say they are, where they’ve been, for how long and how often. We notice their demeanour, their nerves.” It takes experience to spot children being trafficked. E-gates detect fewer suspicious cases.

If members of the public complain about long queues with too few passport desks open, staff issue a reply from a printed sheet they’re given: “All available Border Force officers are currently deployed and working to protect the public; border security remains our number one priority.” An honest reply would go something like this: “We haven’t got enough staff, we’ve had cuts, we’re on our knees working all hours and still missing our targets. Many more passengers are coming through and we don’t have time to scrutinise them. Sorry. Did you vote for these cuts?”

With everyone manning the desks, paperwork piles up behind the scenes: asylum claims are rising again and people stopped can wait hours to be checked. Staff are taken off customs: “Guns and drugs don’t matter as much as queues,” one officer says. They sometimes fail to claim the £2,000 fines from airlines that bring people in with inadequate documentation because they miss a five-day deadline for claims.

Staff hired now are on new contracts, with flexible annualised hours so they can be made to work overtime, extra days or to cancel holidays at short notice, “a nightmare for parents with childcare”, I was told. As a result, there is high turnover. “We’re at least 300 short,” these officers reckon. Managers deny it – but fixed official quotas of staff have been abolished.

Visa checks on people from non-EU countries are weaker, they claim, now visa offices abroad have been closed. “There are no standard interviews for student or visitor visas now. But you can’t rely on written references and qualifications,” says one officer who has worked overseas. “You need to see applicants to detect people who are not what they say they are.” During the present “surge”, there is only one forgery specialist each shift, instead of two or three: “They’re run off their feet.”

This isn’t just staff grumbling: the rightwing, anti-public sector Adam Smith Institute reported last month that the Border Force is “starved of funds and neglected”. Responsible for screening 225 million passengers a year arriving in the UK, it claims about 4,000 “high-risk” flights are landing without proper security checks.

Passenger numbers have risen by 20% since 2010 and are set to continue rising by 2% a year, while Border Force funding is cut: spending per passenger is down 25%. Some technology is 14 years out of date, while £1bn was wasted on a failed e-borders system. Last year’s National Audit Office report warned that the Advance Passenger Information System was collecting only 86% of arrivals. The system cannot check them all “in sufficient time to prevent high-risk travellers from starting their journey to or from the UK,” the report said. That leaves 16.5 million people a year unchecked before arrival.

Brexit will bring far worse problems. Half of all arrivals are from the EU, currently waved through on a scan to check their identity. But plans afoot at the Home Office suggest EU migrants will need to prove they have a skilled job lined up and can speak English. “We would need to check all these jobs were genuine – very difficult and very time-consuming,” says one officer. It might require doubling the Border Force.

“Take back control” was a brilliant play on people’s fears. What the people swayed by it and everyone else should know is that controlling our post-Brexit borders will be phenomenally expensive and difficult. And how closed the UK is going to feel to our neighbours.