More than half of state school teachers would not advise bright pupils to apply to the UK's top universities, and the numbers are falling, research suggests.

The Sutton Trust, which commissioned the study, warned it is deeply concerning that the majority of teachers would not encourage gifted students to apply to Oxford and Cambridge.

It said more needs to be done in schools to "dispel the myths" about the two elite institutions and other leading universities.

The study, which questioned 730 state secondary school teachers, finds that just 44% would encourage their gifted students to consider Oxford or Cambridge, down from 50% five years ago.

A breakdown of the findings shows that 16% of teachers always encourage their academically gifted pupils to apply to Oxbridge, while 28% say they usually do.

The survey also reveals that many state school teachers underestimate the proportion of pupils from state schools that study at Oxford or Cambridge.

Around one in seven (14%) say they do not know.

Of the 86% that gave an answer, more than half (55%) say it was less than 30%, while just 7% say over half of the UK students at Oxbridge were from the state sector.

In reality, 57% of students admitted to Oxbridge are from state schools, the Sutton Trust said.

Trust chairman Sir Peter Lampl said: "It is deeply concerning that the majority of state school teachers are not encouraging their brightest children to apply to Oxford and Cambridge.

"It is also worrying that almost all state school teachers, even the most senior school leaders, think that Oxbridge is dominated by public schools."

He added: "The sad consequence of these findings is that Oxford and Cambridge are missing out on talented students in state schools, who are already under-represented at these institutions based on their academic achievements. We need to do much more to dispel the myths in schools about Oxbridge and other leading universities."

These universities also need to ensure they are accessible to bright students, regardless of background, Sir Peter said.

Brian Lightman, general secretary of the Association of School and College Leaders, said pupils need good careers advice from an independent, qualified adviser.

"We agree that young people should be made aware of the opportunities available to them, which is why we have been so concerned about the removal of national funding for face-to-face careers guidance by a qualified adviser," he said.

"This should be an entitlement for all students. Applying to Oxbridge is only one of many appropriate routes for our brightest young people. There are many good universities in the UK and other excellent employment-based routes into top careers, all of which are available to high-calibre applicants from all backgrounds. Social mobility is about far more than entry to Oxbridge."

Mr Lightman said teachers are not careers advisers and may not know, or have experience of, Oxbridge and their admissions processes.

Careers advisers can tell students "about all opportunities".

"There are many universities that may be more appropriate for some pupils and not for others," he said.