The lost amphitheatre of northern England has been found on a Yorkshire hilltop in a discovery with major implications for the study of Roman Britain.

Centuries of speculation have ended with a printout from geomagnetic scanners which reveals a great tiered bank of seats below curving hummocks in a field now frequented only by a herd of cattle.

Crowning the summit of Studforth Hill, the oval arena would have combined spectacles and entertainments with a magnificent 360-degree view, making it the equivalent of a national theatre of the north.

The find by Cambridge University archaeologists – led by a young woman who grew up locally and was told the amphitheatre legend by her grandfather – seals the importance in Roman times of the small village of Aldborough, between Harrogate and York.

It also adds to growing evidence that Britannia Inferior, as the northern province was known, was busier, more prosperous and cultured than previously thought. There have been a relative shortage of digs and studies of civilian sites in the area, compared with hundreds in Britannia Superior, today's south.

Initial work suggests the amphitheatre was flanked by a sports stadium.

"Its discovery leaves little doubt that Isurium Brigantium, as Aldborough was called in Roman times, was the civil capital of the Britons known as Brigantes, effectively the population between Derbyshire and Hadrian's Wall," said Martin Millett, professor of classical archaeology at Cambridge.

"York is much better-known for Roman remains, in part because it has remained a great city, but the evidence suggests that it was the military base. Civil power and society, and the most important place for Roman Britons in the northern province, was likely to have been here."

The sweeping curve of the amphitheatre, which crowns a long series of discoveries at Aldborough, lay hidden because of changing fashions in archaeology, shortage of money for excavations and pressure for resources to go elsewhere.

Rose Ferraby, who has led a two-year survey of the village with Millett, said: "It was under our noses. I used to come here as a girl with my friends because the slope and terracing made it Aldborough's sledging hill.

"My grandad told me the story of the lost amphitheatre and I got more and more interested through doing odd jobs at the manor house, whose garden has plenty of Roman remains."

The spell cast over her by the village, where no deep digging is allowed without planning permission and all building projects, down to conservatories, have to have an archaeologist on watch, took her from a Harrogate comprehensive to Cambridge and then the British School of Archaeology in Rome.

"The whole of Aldborough – and as much land again around it – is a scheduled monument," she said. "Work over the years has pointed more and more towards the conclusion that it was somewhere very important in this part of the Roman empire. Mosaics have been discovered with inscriptions in Greek, a sure sign of cultured inhabitants. We were certain that there had to be an amphitheatre somewhere."

The breakthrough came with geomagnetic and ground radar in which more than a square mile of cottages and pasture were turned into a grid, which Ferraby, Millett and volunteer students paced with handheld scanners and others examined on a machine akin to a lawnmower. They called locals to a packed meeting this week to announce the amphitheatre had at last been tracked down.

Most of the tiered seats were quarried or hacked out centuries ago, but the high bank which forms the crown of Studforth Hill hides the surviving section. The geomagnetic scan detected a large mass of material and then tiering, which is crudely reflected by ridges in the grassy surface until it disappears under a small copse.

"We don't yet know whether the seats are stone, which would have been the best quality, or a mixture of timber and compacted earth which has been found at other sites in the UK," said Ferraby. "But there are at least four rows and an extra ridge of land behind the trees suggests that there may have been a fifth. Whatever the material, it would have been an imposing building."

Aldborough was thought for years to have been a Roman fort because of its impressive town walls, which include a long remaining stretch with curved lookout towers. The strategic position on Dere Street, up which the ninth Hispana legion marched to its unknown fate in Scotland in about 120AD, also pointed to a largely military function.

But a series of small 19th- and 20th-century excavations, many in gardens and allotments, began to build a more complex picture, and the discovery of the town's Roman name – meaning the "main city of the Brigantes" – shifted opinion towards a large civilian settlement.

This evidence supported theories that the Romans kept their troops in large military bases while encouraging native Britons to build their own towns on the imperial model, with a forum, stone and brick buildings and temples for the appropriate gods, one of the parts of the Aldborough jigsaw still to be found.

The Cambridge team is now completing its geophysical survey of the Roman town's entire site, which will be analysed for possible excavation points, possibly including the amphitheatre, if funding can be found.

Archaeologists hope to combine the scanned data with work by the Landscape Research Centre to allow computer views of underground UK classified by historical period.

"We hope this will be a spur to more exploration of northern Roman sites," said Hillaby. "We probably have an unbalanced impression that more went on in Britannia Superior because archaeologists have spent more time on civilian settlements there. I have no doubt that the amphitheatre spectators, up on the best seats, would have looked out on scores of other settlements between the town and the escarpment of the Hambleton Hills and North York Moors."