Health Secretary Jeremy Hunt on Wednesday apologized for the problems.
Bosses in St Richards in Chichester and Worthing have spoken out amid winter pressures as they're struggling to deal with the number of patients needing treatment.
"With the NHS coming under pressure as never before, we are asking patients and the public to use the health service responsibly to help ensure that care is readily available for everyone who needs it", she said.
She added: "The NHS has been better prepared for this winter than ever before, we have put extra funding in".
This will mean that senior hospital doctors can triage more patients in A&E, be available for phone advice for Global Positioning System and ensure that patients in hospitals are reviewed twice each day to help timely discharges.
Hunt also thanked NHS staff for their "heroic" effort for working "beyond the call of duty".
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Each year the service comes under increased pressure in the winter, largely as a result of an increase in certain illnesses over this period, such as flu.
That is why we are making these further recommendations today.
"The difference between this year and last year was that we had these horrific pressures in January which we've always had... and we had to cancel people's operations at the very last minute".
Officials have estimated that this could lead to up to 55,000 deferred operations, although c ancer operations and time-critical procedures should go ahead as planned, NHS England said.
"Winter is an extremely busy time of year for the ambulance service and the NHS more widely and we will continue to work as a collective with our health board partners to manage increased demand".
He added: "There's a great desire to get politicians to issue certain words, if you want me to say there's "extreme pressure" then I will".
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"Local people can help by not attending A&E for conditions which they could wait and see their GP for".
They also say they're prioritising emergency patients and reviewing non-urgent activities, as well as opening up additional beds.
"Their staff can offer advice as to the best place to get the right care".
Chief Executive Professor Joe Harrison said the move has been undertaken due to high numbers of sick patients being admitted, and fewer patients being able to be discharged.
'This is an unparalleled situation in Lanarkshire and exceptional circumstances need exceptional measures to enable us to deliver our number one healthcare priority - patient safety'.
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