Inspectors from the country's independent regulator for health and social care have told Arrowe Park and Clatterbridge hospitals they must make improvements across several key areas.
A new report from the Care Quality Commission has raised concerns about emergency services, maternity and end of life care among others.
A lack of staff on duty with the right skills at the right times was also highlighted.
However the hospital trust were rated "Good" for providing caring and effective services.
Inspectors found staff were caring and worked hard to ensure patients were treated with dignity and respect.
Chief Inspector of Hospitals Professor Sir Mike Richards said: "While I am satisfied the trust is heading in the right direction there is much for it to do to implement its improvement plans and secure more positive outcomes and experiences for patients."
The report published today shows:
Urgent and emergency services: Requires improvement.
Medical care: Requires improvement.
Critical care: Requires improvement.
Maternity and gynaecology: Requires improvement.
Services for children and young people: Requires improvement.
End of life care: Requires improvement.
Wirral hospital trust chief executive David Allison said the rating was “as expected” and thanked the CQC for acknowledging "the journey of improvement currently taking place at Wirral hospitals with its 'dedicated' and 'caring' staff at the forefront of its recovery."
Mr Allison said: “The CQC’s report highlights many areas of good practice across the trust.
"This rating was also in line with our own self-assessment, highlighting that we know exactlywhere we want to improve and how we can achieve this.
"I am reassured that the CQC, which recognises the highest possible standards, fully endorsed our own self-assessment.
“Three quarters (75%) of all health and social care organisations inspected by the CQC are now rated as ‘requires improvement’, and this reflects the challenge to meet those very high standards.
“It is encouraging that the report found that services were provided by dedicated, caring staff and patients were treated with dignity and respect. I am also pleased that patients were positive about their interactions with staff who they found to be open, honest and helpful.”
Wirral hospital trust chief executive David Allison
The team of inspectors and specialists - including doctors, nurses and managers - inspected the hospitals over four days during September 2015 and conducted an unannounced inspection on September 24.
They found staff were positive about working for the trust and the quality of care they provided.
The trust had made a positive response to a previous CQC inspection and recruited more nurses to ensure safer staffing levels - but staffing is still a problem in some areas.
There were still times when medical wards were not appropriately staffed.
This was a concern on Ward 36 at Arrowe Park Hospital and during the night at the Clatterbridge Rehabilitation Centre.
The trust was found to be led and managed by a visible executive team.
The senior team was known to staff and it was evident that in response to a disappointing staff survey it had made considerable efforts to engage and include staff in the plans for change and improvement.
Lack of readily available beds in medical wards affected the patient flow within the emergency department.
Inspectors found delays in admitting patients to the emergency department within Arrowe Park.
This meant the emergency department was often full and could not immediately treat new patients.
The number of ambulances waiting more than 30 minutes over patients had reduced significantly since the introduction of a rapid assessment and treatment area.
The inspection identified several areas for improvement, including:
Ensuring that there are adequate numbers of suitably qualified staff in theatre recovery areas to ensure safe patient care.
Ensuring the children’s safeguarding training meets Royal College of Paediatrics and Child Health guidelines 2014.
Ensuring that robust information is collected and analysed to support improvements in clinical and operational practice.
Ensuring risks are always managed and mitigated in a timely way.
The reports highlight several areas of outstanding practice including: Inspectors observed staff displaying a very caring, person centred attitude which went beyond what was expected.
Staff encouraged patients and their relatives to be active partners in their care and went "above and beyond" to meet patient’s preferences.
There were strong relationships between staff, patients and their relatives.
A nutritional risk assessment was in place and consistently used by staff to determine patients’ individual needs.
The sentinel stroke national audit programme latest audit results rated the trust overall as a grade "A" which was an improvement from the previous audit results when the trust was rated as a grade "B."
Professor Richards added: "The trust has listened to our inspectors’ latest findings and already begun to take action where it is required.
"We will return in due course to check that the improvements needed have been made and are embedded.”
The commission will present its findings to a local "quality summit" - including NHS commissioners, providers, regulators and other public bodies - to develop an action plan and make recommendations based on the inspection report.