New admissions at the trust, which includes Dewsbury and District Hospital, increased from 15 in the week ending June 5 to 33 in the week ending June 12.
The 33 per cent rise in a week comes amid growing concern over two Omicron sub-variants, BA.4 and BA.5.
The steepest rise was seen in the North West, where 741 people were admitted in the week to June 14, up 55 per cent from the previous week.
The North West also has the highest rate of hospitalisations, at 10.5 per 100,000 people.
In the North East and Yorkshire, 770 people were admitted to hospital in the week to June 14, up 30 per cent on the week before.
Most cases in the UK are still caused by the Omicron BA2 variant, originally dubbed "Stealth Omicron", UK Health Security Agency (UKHSA) data shows
But health chiefs are monitoring the impact of the variants Omicron BA.4 and Omicron BA.5, which were designated variants of concern in the UK on May 20.
Dr Mary Ramsay, director of clinical programmes at the UKHSA, said: “After a period of low case rates, we are now seeing increases in outbreaks within care homes and in hospitalisations among those aged 80 years and over.
“It is encouraging that we are not seeing an increase in intensive care unit (ICU) admissions but we are monitoring data closely and assessing the possible impact of subvariants BA.4 and BA.5.
“As we enter summer, it’s still important to remember that Covid-19 has not gone away and to get vaccinated to reduce the risk of becoming seriously ill with the virus.
"If you’re not yet up to date with your jabs please come forward now – it’s not too late to get protected.
“Remember to observe good hand and respiratory hygiene. It is also sensible to wear a face covering in crowded, enclosed spaces.
"If you have any symptoms of a respiratory infection, and a high temperature or feel unwell, try to stay at home or away from others – especially elderly or vulnerable people.”