Striking health workers will attempt to gain support at the Labour Party conference in their bid to block the sell-off of the NHS supply agency.
Staff are "angry and disappointed" at the sell-off of NHS Logistics
Hundreds of workers are taking part in their second 24-hour strike over the transfer of NHS Logistics to German delivery firm DHL.
Unison is expected to propose a motion at the Manchester conference calling for a review of NHS privatisation.
The government said disruption from last week's walkout was minimal.
A Department of Health spokesman said there had been no reports of any major problems, and hospitals and GPs had contingency plans in place - many can also order their own supplies, rather than go through NHS Logistics.
And he added the transfer, which takes place at the beginning of October, would "help save £1bn over 10 years".
Karen Jennings, head of health at Unison, said it had never been the intention to disrupt patient care.
She told the BBC: "Our members could have taken two days, they could have taken three days, but they didn't want to damage patient care in any way, shape or form, so the impact thankfully has been minimal."
NHS Logistics supplies about 50,000 lines of products, including bedpans, latex gloves, syringes, bandages, medical equipment and food.
The deal prompted hundreds of workers to go on strike last week in the first national NHS walkout for 18 years.
Staff from the five depos across England were repeating the strike on Tuesday and into Wednesday.
It comes after Unison dropped its plans for a judicial review over the transfer.
But union leaders are still hopeful the strike, which could be followed by further industrial action, will still put a halt to the deal.
Unison said fears were growing among staff that their pay and employment conditions will be affected following a separate dispute involving DHL's own workforce.
Thousands of drivers and other employees are being balloted for strikes in a dispute over pay and jobs.
Dave Prentis, general secretary of Unison, who will be visiting one of the picket lines in Runcorn overnight, said the new dispute had heightened fears among Logistics workers about their future employment.
He has written to Health Minister Andy Burnham warning of the "growing concerns" by NHS Logistics workers and revealed that no written agreement had been reached between Unison and DHL over terms and conditions.
He claimed the company failed to turn up for a planned meeting last week and called on the government to confirm how guarantees on jobs, pensions and employment will be given.
He will also table the motion at the Labour Party conference on Wednesday.
Mr Prentis added: "Our members at NHS Logistics fear for their jobs and the service they provide to hospitals and GP surgeries."