Hospitals and retailers were given until the end of March to reduce the number of sugary soft drinks, milkshakes and hot drinks with added sugar syrups, to 10 per cent or less of all beverages sold across its sites.
However NHS England said that 80 out of 232 trusts have not yet joined the voluntary programme and warned that a ban could come into effect on July 1.
The health body has already changed the hospitals' contract to allow the complete prohibition of sugary drinks by the summer.
NHS England chief executive Simon Stevens said: "We now know that obesity causes 13 different types of cancer as well as heart attacks and strokes, so the NHS has needed to get its own house in order on the epidemic of flab.
"Once the Easter eggs are gone, the NHS will be getting on with ensuring our hospitals and their retailers are offering healthier food and drinks for patients, relatives and staff."
The new figures come ahead of the introduction of a tax on sugary soft drinks on Friday.
Campaigners said some hospitals may still be stuck in long-term contracts with suppliers that they were struggling to get out of.
National suppliers including WH Smith, Marks & Spencer and Greggs have signed up to the NHS voluntary scheme to cut sales of sugary drinks, along with 152 of 232 trusts.
Last year, Mr Stevens also ordered hospitals to remove super-size chocolate bars and "grab bags" of snacks from sale in a bid to tackle obesity.
NHS England said some hospitals had made good progress including one large snack retailer which had sold 1.1 million fewer single chocolate bars last year and increased fruit sales by 175,000.
The changes have led cafe chain Costa to stop selling the largest size of some of its drinks in hospitals, while thousands of chocolate bars have been removed from shelves and several retailers have been encouraged to reduce the number of calories in sandwiches, NHS England said.
Professor John Wass, from the Obesity Health Alliance, said NHS England was "leading by example when it comes to tackling obesity".
"The reduction in sales of unhealthy food and drink in hospitals is an important step in the battle against obesity," he said.
"It also sends a strong message that the NHS is serious about cutting the amount of sugar in the nation's diet."
Professor Jonathan Valabhji, National Clinical Director for Diabetes and Obesity, at NHS England said: “We have been clear that the growing obesity crisis sweeping the country is a public health crisis and the evidence backs it up.
“ Obesity is associated with heart attacks, cancer, Type 2 diabetes and a number of other illnesses – causing personal suffering and costing the health service and in turn the taxpayer, billions every year.
And for all of those conditions, wherever possible, prevention is preferable to cure. Our own sugar restrictions, the new sugar tax and the NHS diabetes prevention programme are all part of what needs to be a concerted effort to address obesity.”