The testimonies include one from an RAF officer who took part in the 1944 Great Escape and the daughter of resistance heroine, Violette Szabo.
About 4,000 people applied to the UK Foreign Office in 1964-65 for help from a £1m fund, paid for by West Germany.
A quarter of claims were successful.
Many were rejected because, though the claimants had suffered under the Nazis as prisoners of war or civilian internees, their imprisonment had not been illegal. Others were rejected because they were not British citizens.
The archives contain often brutal accounts of suffering and persecution, as well as the responses of Foreign Office bureaucrats charged with administering the fund.
The money was aimed principally at concentration camp survivors who had not won compensation under a separate German scheme set up in 1953.
Among those whose claims were rejected was Jimmy James, who took part in the Great Escape from Stalag Luft 3 in 1944 - made famous in the film of the same name. Fifty of the escapers were shot.
Jimmy James, along with others, was sent to a punishment camp known as Sonderlager A at Sachsenhausen concentration camp, north of Berlin.
By 1964, his file shows he was working for the Foreign Office as a visa officer at the British Embassy in Prague.
The file includes his handwritten account of his years in Nazi captivity, including his imprisonment with 18 others - six of them British - at Sachsenhausen - and a period spent in solitary inside the main camp when he once again tunnelled his way out, only to be recaptured.
He acknowledged the conditions he was kept under were not as harsh as those in Sachsenhausen proper, and that he could claim no permanent disability, before adding laconically, "although, naturally, this is an experience which I should have preferred to have avoided".
His claim was rejected on the grounds that as a prisoner of war he was not a victim of "Nazi persecution".
But there was a sequel.
Some of his fellow "Great Escapees" went to the newspapers to complain and the foreign secretary set up an inquiry which resolved on pay-outs to the Sachsenhausen victims after all.
All were officers and two bore the name Churchill.  In 1968 James got a cheque for £1,192 and 15 shillings.
That emboldened others to underline their own claims.
Another file contains correspondence with an anonymous former soldier in the Cameron Highlanders regiment. The names of people in many of the files have been blacked out, or redacted, on data protection grounds.
In 1964 he had applied for compensation, describing himself as "an incorrigible escaper and troublemaker" who had "suffered persecution in four punishment camps".
His claim was rejected.
In 1968 he wrote a long and outraged letter in the wake of the Sachsenhausen decision.
It reiterated his prison camp record, the ill-treatment he had suffered and the effects on his health, adding that he had also spent time in Buchenwald.
"Do I need to appeal to the House of Lords like the elite who were awarded this money?" he asked.
The Foreign Office asked the German authorities and the Red Cross for evidence that he had been in Buchenwald, but they could find no record, and when the man himself was asked for further details he never replied.
But someone who did get compensation was Tania Rosandic, the daughter of Violette Szabo, an agent of Special Operations Executive who died in Ravensbruck concentration camp. Szabo's experience was also later reflected in a film - called Carve Her Name with Pride.
A friend of Tania Rosandic's mother's wrote from Ireland to press the girl's claim, which was accepted, but not before her solicitors had to find not only her mother's French birth certificate but also her grandfather's, to prove she was British.  She got a total of £2,295 and 15 shillings.
Several of those who applied for compensation were Channel Islanders who had been arrested by the Nazi occupiers and taken to Germany as forced labourers.
Harold Le Druillenec, from Jersey, ended up in Bergen-Belsen. He was the only British survivor.
"Jungle law reigned," he wrote of the camp.
"At night you killed or were killed; by day cannibalism was rampant."
He spent his days heaving bodies into mass graves, though too weak himself to dig the holes, and later gave evidence at the war crimes trials of Belsen's commandant and guards.  He was awarded £1,835.
But others were not successful. Ludmila Kokrda spent five-and-a-half years in Nazi custody, including a year in Ravensbruck concentration camp.
She was forced to work on clearing a swamp, often in heavy rain, wearing nothing but a cotton shirt and living on a diet of beetroot or beetroot leaves and potato peelings.
But she and her husband - a Czech army colonel who had fought in both world wars and had fled to Britain twice to escape both the Nazis and later the communists - were not British citizens.
Their application was rejected, despite the fact that the Liberal Party leader Jeremy Thorpe had taken up their case.
Harrowing accounts of Nazi persecution against UK victims have been revealed in 1960s files from the National Archives, which show them claiming compensation for their suffering.