Schools in poorer areas are struggling most to recruit teachers and 85 per cent of staff say the problem is impacting quality of education, according to the report, The Recruitment Gap.
By comparison, 55 per cent of teachers at independent secondary schools and 76 per cent at state schools in the most affluent areas said they were concerned about recrutiment impacting the quality of education.
However, around half of teachers would apply for a job at a low-performing school if they were offered a substantial promotion, leading the charity to recommend that schools in disadvantaged areas should be encouraged to spend Pupil Premium income on teacher wages and professional development.
Almost a third of teachers in the most disadvantaged schools said they expected appointments to be made that were not well matched to their vacant posts.
Some 25 per cent said they anticipated serious recruitment difficulties or were certain they would have to end up using teachers that were not suitably qualified or supply staff.
Researchers surveyed 3,000 primary and secondary school teachers between April and June using an app which asked them daily questions about how recruitment difficulties and teacher shortages affected their school.
The report states: "Of the key factors likely to attract them to work at the school, many cost relatively little money."
For the half of respondents (49 per cent) that said they would be attracted by a substantial promotion, this could cost schools £5,000 per staff member, depending on the starting position of the teacher.
A similar proportion (48 per cent) said they would be interested if they had a guaranteed reduction in their teaching timetable of around 25 per cent, likely to cost around £10,000.
In addition, more than half (54 per cent) said they would consider applying for a job at a low-performing school if there was a clearly enforced and effective behaviour policy.
However, one in five teachers indicated that nothing would encourage them to apply for a job at a low-performing school that had recently gone into special measures.
While spending on recruitment is already allowed under pupil premium guidelines, this should be emphasised further in line with the new Education Endowment Foundation pupil premium guidance which "signals this strongly", the report states.
Sir Peter Lampl, the charity's founder and executive chairman, said recruiting and retaining high quality teachers was the biggest challenge faced by schools.
"As our research shows, it is disadvantaged schools that are most affected by the lack of high quality teachers," said Lampl, adding: "We would like to see more schools using their Pupil Premium to recruit and retain good teachers.
"There should also be increased effort to address behaviour concerns.
"This is a major obstacle to recruiting good teachers to disadvantaged schools."
Maths and science at secondary schools showed the greatest shortages, with around one in three departments in the most deprived areas reporting that they were not well-staffed.
The report makes a further recommendation that the government should monitor social inequalities in teacher recruitment since not all schools were equally affected by teacher shortages.
It should also consider requiring teachers in receipt of substantial bursaries to teach in more disadvantaged schools or in particular areas as a condition of the bursary.
"This would need to be done with care, ensuring that a place at one of these schools was indeed available to the trainee teachers and that the school was able to provide them with the sort of environment where they were able to thrive," it states.
James Zuccollo, director for school workforce at the Education Policy Institute, believes getting high quality teachers into hard to staff areas is one of the biggest policy challenges facing the Department for Education.
"This report echoes our own research, which shows that many disadvantaged schools in England are facing acute shortages of highly-qualified teachers," said Zuccollo.
"This is a particularly severe problem in subjects such as physics and maths, which are deemed top priority by the government.
"Outside of London, fewer than one in five physics teachers in the most disadvantaged schools have a relevant degree, compared to one in two in the most affluent schools."
Zuccollo is supportive of paying supplements for teachers in shortage subjects, "particularly for those teaching in the most disadvantaged areas", adding: "The government has considered this policy in its new teacher recruitment and retention strategy, and will be hoping that it is able to quickly improve on the current outlook, and support those areas of the country that have been left behind."