The body of an unidentified man recovered from the sea off north Wales 30 years ago will be exhumed this month in the hope that it can be returned to his family.

The exhumation, from an unmarked grave at Menai Bridge cemetery, on Anglesey, is part of a nationwide attempt by police forces around Britain to put names to more than 1,100 unidentified bodies dating back to the 1950s.

The national Missing Persons Bureau, which is the driving force behind the work, has established a website containing images and identifying features of the individuals who have remained nameless for so many years, in the hope of closing some of the cases. The site is one of only a few such facilities in the world.

As well as 1,029 men and women, the site contains details of 105 babies in unmarked graves, unclaimed by families, sometimes for decades.

They include an infant known as the Burythorpe baby, a boy of around 34 weeks' gestation who was found wrapped in plastic bags at Burythorpe Bridge in North Yorkshire in January 2001. Forensic tests established he had died two years earlier, but despite extensive inquiries his parents have not been traced.

Some of those who remain unidentified drowned in rivers; others were found in abandoned outbuildings, under railway bridges or by the roadside.

In most cases, the only clues to who they are come from identifying features on their bodies, such as a broken ankle or a tattoo, or their possessions – in one case, a pair of gold-rimmed reading glasses in a black case.

Joe Apps, manager of the Serious Organised Crime Agency's UK Missing Persons Bureau, said: "For us it is about asking how we can be in such a developed society and yet have such a large collection of unidentified people, when it is actually quite difficult to disappear nowadays. So how is it we haven't been able to recognise these people? There will be a family that is missing someone and it is right they know where their loved ones are."

The work relies to a large extent on developments in DNA testing, which could at last give some of these individuals identities. But it is painstaking work and, so far, only about eight bodies have been identified.

There are hopes that in the coming weeks the man buried in Anglesey will join that list after contact was made with the family of a missing Norwegian seaman.

The evidence was strong enough for the north-west Wales coroner to sign an exhumation certificate, and later this month the operation, involving police and forensic experts, will take place. Detective constable Don Kenyon, who is running the investigation, said it was a "rare and sometimes sensitive process".

"The circumstances surrounding this man's death are not suspicious – we are merely attempting to identify him for his family's sake," he said. "That process will involve carefully obtaining DNA samples and comparing them against the DNA from individuals we have identified as possible family members."

In Norfolk, the family of Michael Sutherland were able to hold a memorial service for him late last year, 23 years after his body washed up on a north Norfolk beach. When an investigation failed to identify him, villagers in Weybourne held a funeral service and buried him in the churchyard.

But detectives took a fresh look at the case as part of their review of unidentified bodies in Norfolk and Suffolk, and exhumed the body to retrieve a DNA profile. Crosschecked against the missing persons database, the profile matched that of Michael Sutherland.

His sister Ann Stockton, from Cleethorpes, travelled to Norfolk last November with other members of the family for a long-delayed dedication.

Thames Valley police has used a forensic artist to draw eight individuals whose bodies were found in Buckinghamshire, Oxfordshire and Berkshire since the 1970s.

Detective Sergeant Craig Kirby, of the force's major crime review team, said: "This is the most significant work we have done and it fits into the national picture. As police, there is nothing more important that we can do than to bring resolution to families, either within the criminal justice system or working with the coroner to identify people that we find."

Retired detective Andy Steel investigated one of the eight: a body found trapped in weir gates in the Thames at Sonning Lock on 2 January 1995. He still has the log he recorded that morning.

"It was a frosty morning, the body was trapped in the weir," he said. "He had been in the water for some time. We called in a search team and took the body to hospital for forensic tests.

"We took certain items from the body. The most important to my mind was a lovely pair of glasses, which folded into themselves and fitted into a black pouch.

"I remember thinking then: 'Oh, we will identify this chap for sure'." But 18 years on, the unnamed man – aged between 30 and 50 – has never been claimed.

The body had been in the water, police estimate, for up to 18 months and was badly decomposed. Police obtained a dental outline and circulated the details to dentists across the country, but there were no leads.

"We trawled through the missing persons database but there was no one fitting his description," said Steel. "We made several appeals, but no one came forward to say that looks like my father, or grandfather.

"These things stay in your mind. It is the only case in my career that remained unresolved and I am hoping this latest publicity might resolve it."