Nockolds Solicitors said it found that the average payout over the 2017/18 financial year was £158,219 but some trusts paid out more than £1m each.
It said routine breaches of the duty of care the NHS owes to its staff and hospital visitors often get overlooked because of the focus on compensation for medical negligence.
NHS trusts paying more than £1m included North West Ambulance Service NHS Trust (£1,076,909) and Guy's and St Thomas' NHS Foundation Trust (£1,009,306).
Last year 232 trusts paid out a total of £34,966,393 to settle employers' liability, public liability, property damage and theft claims.
The firm said this amount does not include claimant or defence legal costs and is simply the aggregate sum paid to claimants as a result of hospitals failing to provide adequate safeguards for staff and members of the public.
Trusts paying out more than £600,000 included The Christie NHS Foundation Trust (£771,925), Royal Free London NHS Foundation Trust (£672,579), Barts Health NHS Trust (£632,306) and University Hospitals of Morecambe Bay NHS Foundation Trust (£627,419).
Examples of employers' liability claims include slips, trips and falls, accidents caused by defective equipment and as a result of insufficient training or supervision.
Public liability claims include hospital visitors slipping, tripping or falling within hospital grounds or public areas.
The details come from freedom of information requests to all 232 trusts in England.
Seven trusts had no payouts last year, including Great Ormond Street Hospital for Children NHS Foundation Trust, Royal Marsden NHS Foundation Trust and Papworth Hospital NHS Foundation Trust.
Rachel Davis, personal injury specialist at Nockolds Solicitors, said: "Accidents happen but they should not be happening on this scale.
"Doctors, nurses and other hospital staff have the right to work in a safe environment while members of the public should not be at risk of injury during routine visits to family and friends.
"Public liability claims arise when members of the public are injured in a public place because those responsible for the area have failed to ensure it is safe. The legislation places a duty of care on the NHS to protect members of the public visiting their premises.
"Employers' liability claims occur when an employer breaches its duty of care to provide a safe working environment for staff. Like all employers, the NHS has a duty to their employees and should take all reasonable steps to ensure their health, safety and wellbeing."
Ms Davis said such claims often escape attention because of larger settlements for patients who sustain life-changing injuries as a result medical negligence.
"Just as importantly, and as a matter of principle, NHS staff going about their work and members of the public making hospital visits should not be exposed to dangerous risks and injury through no fault of their own," she added.