The Romanian ambassador to the UK has said his country has made a significant financial contribution to the NHS as a result of the number of highly qualified health workers who have moved to Britain.

Dan Mihalache said his country paid more than €100,000 to train up one medical student to become a doctor in Romania.

“That is our contribution to your National Health Service,” he told a committee of peers in the House of Lords, adding that there were 10,000 or more Romanians working in the NHS.

Mihalache argued that there were “two sides of the coin” when it came to free movement within the EU, “one good and one bad”.

The positive impact for Romania was that its citizens working abroad across the world sent back €7bn in a good year, and between €3bn and €4bn during the economic crisis.

But both he and the Polish ambassador, Arkady Rzegocki, said their governments had considered policies to stem the loss of skilled workers, including ideas around making graduates work for a number of years or pay back the cost of their courses.

“Of course we are worried about that,” said Rzegocki, who said there were 1 million Poles living in the UK, with the vast majority in employment or studying.

“We hope that they will start to be coming back. I hope that the situation will improve because we’ve had a huge economic success ... our GDP is growing every year.”

He said an improvement in benefits for children in Poland, bringing the levels almost up to those given out in Britain, had persuaded people to remain in the country, and said the numbers coming to the UK had fallen over time.

The men were appearing in front of the Lords’ EU justice committee, which is carrying out an inquiry into the impact that Brexit could have on the acquired rights of EU migrants in the UK and British migrants elsewhere.

Rzegocki said there had been concern about reports about hate crime against Poles, although he had tried to reassure people that the incidents were few in number. He said he wanted people to have better knowledge about Poland including its contribution during the second world war.

But he said the biggest problem with Brexit was the uncertainty faced by Polish citizens. “They are asking about their future, the future of their children, the NHS,” he said, arguing that not knowing what might happen was not good for individuals or the economy.

Mihalache said that Romanian citizens had been calling his embassy to express similar concerns, including asking questions about their status, rumours that they could be expelled, and questions about permanent residence.

“What will happen to people who paid their social contributions here in United Kingdom? What will happen to the mechanism, will payments made in UK be paid back – do they have to have registration certificates?” he added.

The ambassador added that the “rhetoric” he had heard about registering foreign workers, along the lines of Amber Rudd’s proposals for a visa scheme post-Brexit, “are not encouraging for our communities”. The men said their plea was for all existing rights for their citizens to be protected.

Lady Kennedy of the Shaws, who chairs the committee, said she had set up the inquiry after hearing that embassy phone lines had been jammed by EU citizens asking “what is going to happen to us? We have bought a house, our children go to school, how do we learn our futures?”.

The committee will present its recommendations by the end of the year.