Morale among NHS medics and care workers from the EU has been hit by the uncertainty of Brexit, the Health Select Committee has warned.
The MPs said around 150,000 workers in health and social care faced an uncertain future because of the decision to leave the European Union.
The cross-party committee also warned that the impact of Brexit on the healthcare of Britons living in or travelling to the EU "should not be underestimated" - with threats to the European Health Insurance Card (Ehic) and challenges for pensioners living on the continent.
Some 60,000 people from EU countries work in the English NHS, with a further 90,000 in adult social care roles.
Theresa May has said she will not give a guarantee on the rights of EU citizens in the UK until reciprocal protection is offered for Britons in other European countries.
The committee said: "The impact of Brexit on the morale of R-EU (the remaining 27 members of the European Union) staff is concerning and the uncertainty they face is unwelcome.
"Difficulties in negotiating the process of applying for permanent residency in the UK and bureaucratic hurdles such as the requirement for comprehensive sickness insurance all add to the concerns of EU workers and their families.
"The Government's plan for our post-Brexit future should both ensure that health and social care providers can retain and recruit the brightest and best from all parts of the globe and that the value of the contribution of lower paid health and social workers is recognised."
The report also warned: "The impact Brexit will have on people who rely on the EU's reciprocal healthcare arrangements should not be underestimated.
"Not only would travellers and holidaymakers potentially lose cheap and easily accessible care provided under the European Health Insurance Card, we heard in evidence that retired British citizens in the EU, disabled people, and people with multiple conditions could face particular challenges.
"The Government wishes to maintain the arrangements largely as they operate at present but no guarantee can be provided that this will happen.
"Consequently people both here and in the EU face uncertainty about their future healthcare arrangements."
The committee said it was vital that ministers and officials from the Department of Health should form part of the UK's Brexit negotiating team when relevant issues were being discussed.
The committee found that England will not be self-sufficient in its supply of doctors "until the end of the next decade at the very earliest", meaning the NHS will continue to require medics from overseas.
"Even if the English NHS becomes self-sufficient in terms of initial training, we will still rely on (and benefit from) the skills and experience of overseas trained doctors who wish to build their careers here," the report noted.
British Medical Association chairman Mark Porter said: "For the thousands of European doctors working in the UK, Brexit has led to anxiety and uncertainty as to whether they and their families will have the right to stay here.
"Almost half of the 10,000 European Economic Area doctors working in the NHS are considering leaving the UK in light of the referendum, which would seriously impact patient care across the country and only increase what are often already unacceptable delays for treatment.
"The committee has also cast a shadow over Jeremy Hunt's plans by recognising that England will not be self-sufficient in its supply of doctors until the end of the next decade at the very earliest.
"As we have said all along, it won't be a case of losing doctors from the EEA and replacing them with British doctors - it takes at least 10 years to train a doctor, and poor workforce planning by the Government means we simply don't have enough for the number of patients in need.
"The NHS is at breaking point and already cripplingly understaffed in many areas such as A&E and general practice. Closing our borders to medical staff from anywhere overseas would be terrible for patient care."
Royal College of Nursing general secretary Janet Davies said: "Theresa May has been told by this cross-party group that failing to give EU nursing staff and others the right to stay will harm the NHS.
"The report leaves the Government with no place left to turn."
She added: "In this election, all political parties must reassure EU nursing staff working in the NHS and social care that they are needed, valued and welcome.
"The failure to do so means soaring numbers are heading for the door.
"We can ill afford to lose their skills."
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