The Home Secretary told her party's conference that immigrants can make it "difficult for schools and hospitals and core infrastructure like housing and transport to cope".
But increases in the number of immigrants typically shorten waiting times in their areas, despite public perception that they are why the health service is overburdened, according to a recent paper published by Oxford University's Blavatnik School of Government.
A 10% increase in the number of immigrants shortened the waiting time for outpatient referrals on average by nine days, the research found
The research measured immigration using the Labour Force Survey in more than 100 areas in England and found, on average, a 10% increase in the number of immigrants shortened the waiting time for outpatient referrals by nine days.
The paper says this is due to the "healthy immigrant effect" - they are more likely than British-born people to be well and be working and, by extension, paying taxes. More people also means more money is allocated to local services.
"Your population increases, so you get more funding but you get healthier people in your area," Carlos Vargas-Silva, one of the paper's authors, told The Huffington Post UK. "More resources, healthier people."
He added the impact immigrants had on services on and infrastructure was defined by how quickly the government reacts to their arrival and invests rather than, as Mrs May suggested, the numbers of immigrants there.
"The important thing is for the local area to get the resources quickly," he said. "It's how fast can the government react to changes in population size. If that happens relatively quickly, then there's no impact or there could be a positive impact. You're getting healthier people into the region, then the region gets money because the population increases but waiting times overall decrease as a result."
The research found that, between 2004 and 2007, there was an increase waiting times in deprived areas outside London, thanks in part to the arrival of many eastern European immigrants. But the increase "disappeared" by 2007 because of more resources were invested to cope with the population increase, Prof Vargas-Silva said.
He added: "[The level of investment] will determine whether you have a negative effect or not... immigrants are not necessarily a burden, it's just how quickly can the government respond and assign resources and then the affect in the medium term can be positive."
When asked which part of the paper he had found the most surprising, Prof Vargas-Silva said it was the fact that the number of immigrants did not appear to have any affect on A&E waiting times.
He said: "If you look on the news, you will see a lot of stories about migrants increasing waiting times... So it blames migrants. We didn't find any impact.
"You have more migrants, there's more use but there's also money and more resources, so the two things go together."
He added that, as an economist, he could not comment on Mrs May's comments about "social cohesion".
When Theresa May spoke at the Conservative Party Conference, she said: "Because when immigration is too high, when the pace of change is too fast, it's impossible to build a cohesive society. It's difficult for schools and hospitals and core infrastructure like housing and transport to cope."
Rob McNeil, a spokesman for immigrant analysts Migration Observatory at the University of Oxford, said: “The concept of ‘social cohesion’ is vague, at best, and there is no consensus on how to measure it.
"So it is very hard to prove or disprove a claim that it has been affected by migration – or indeed any other factor. This isn’t to say that migration has no effects on social cohesion, but rather that the impact depends on what you are looking at."
Lib Dem leader Tim Farron said Mrs May's comments were whipping up "fear and mistrust".