The steps are taken due to concerns over priority services, amid staff shortages caused by Covid.
Critical incidents have been declared at six hospital trusts amid rising staff shortages due to Covid-19.
University Hospitals of Morecambe Bay, which serves Lancashire and South Cumbria, is the latest trust to take the step “to protect services”.
Critical incidents are declared when health bosses are concerned they cannot provide priority treatments.
Prime Minister Boris Johnson said on Monday he would “make sure that we look after our NHS any way that we can”.
Chief executive of University Hospitals of Morecambe Bay, Aaron Cummins, confirmed in a statement that the trust had declared a critical incident.
In an internal message to staff shared on Twitter, Mr Cummins said: “Sadly, despite everyone’s best efforts, many of our patients are still receiving a level of care and experience that falls below the level of standards we would like.”
He also stated that some non-urgent operations and procedures would be suspended.
Mr Cummins said the escalation “allows us to be able to take additional steps to maintain safe services for our patients and help us cope with the growing pressures”.
United Lincolnshire Hospitals NHS Trust said on Monday it had taken similar measures at its hospitals across the county.
Its medical director, Dr Colin Farquharson, said there were “significant staffing pressures due to absence related to Covid-19”.
But he said essential services “remain fully open”.
Chris Hopson, the chief executive of NHS Providers, which represents trusts, said a critical incident was “an indication of very serious pressure” at a trust which may “not be able to provide” a range of priority services.
The chief executive of the NHS Confederation, Matthew Taylor, said that “in many parts of the health service, we are currently in a state of crisis”.
He wrote in a blog, published on Monday: “Some hospitals are making urgent calls to exhausted staff to give up rest days and leave to enable them to sustain core services.”
Many hospitals have been forced to ban visiting on wards in a bid to reduce the spread of the Omicron variant by visitors.
Boris Johnson has warned “considerable” pressure on the NHS is likely to last for weeks to come and said it would be “folly” to think the pandemic was almost over.
A further 157,758 lab-confirmed Covid-19 cases were recorded in England and Scotland on Monday, the government said.