The biggest national strike in the NHS for almost 20 years got under way last night when hundreds of workers joined a walkout in a row over privatisation.

Staff at NHS Logistics will strike for 24 hours in protest at their jobs being transferred to the German delivery giant DHL, and will stage another stoppage during next week's Labour Party conference in Manchester to put pressure on the Government to reverse the lucrative 10-year contract.

Unison said there would be picket lines at five distribution centres and that they expected strong support from other health workers and the public. Its general secretary, Dave Prentis will visit a picket line in Maidstone in Kent tomorrow morning and will press home his complaint that the contract with DHL will cost more money. He warned that the service would get worse. "I doubt if any savings will be made, in fact it will cost far more money," he said.

Unison said last night that it believed the strike would have an immediate impact on hospital supplies and have a cumulative effect as the dispute continued.

But the Government said that it believed the industrial action would only have a minimal effect and patients should not be worried.

Unison warned that hospitals would quickly run out of bulky items such as disposal bed pans and run short of hand gel, latex gloves and food such as breakfast cereal.

The strike hit distribution centres in Derbyshire, Cheshire, West Yorkshire, Kent and Suffolk.

Unison is also planning a legal challenge next week in an attempt to overturn the DHL contract.