As cameras flashed and a video crew dangled its microphone just above his head, Keith Vaz welcomed Britain’s newest immigrant. Shaking Victor Spirescu by the hand, the chairman of the Home Affairs Select Committee peppered him with questions about his plans.

“I don’t come to rob your country,” the 30-year-old assured Mr Vaz, and the gaggle of reporters. “I come to work and then go home.”

It was 1 January 2014 – the first day Romanians and Bulgarians were granted unrestricted access to the UK – and Mr Vaz had come to Luton Airport to greet some of the first arrivals in person. He even took some for coffee.

Not every arrival since then has been so well charted – or charted at all.

Now concerns have been raised that Britain’s official system of measuring immigration – based on a survey initially designed to count tourists rather than migrants – could be significantly understating the number of people moving from the European Union to live and work in Britain.

Critics of the system have highlighted a difference of more than 1.2 million between the official figures for the number of EU nationals moving to Britain in the past five years, estimated by the Office for National Statistics (ONS), and the number of National Insurance numbers issued to those from the EU during the same period.