The influence of teacher encouragement appears to be much greater on students whose own parents never progressed past compulsory education -- an important indicator of a less advantaged background.
For students from these backgrounds, encouragement increased entry into post-16 education from just over half to around two-thirds.
The research also found that encouragement from a teacher has the greatest influence on those students most likely to be on the margin for university attendance.
The University of Cambridge study used 'big data' techniques to look at the long-term impact of student-teacher rapport, and is the first to analyse the role it plays in university access.
The findings, published in the journal Research in Higher Education, show that further education and social mobility policymaking might benefit from increased focus on the "relational aspects" of interactions between teachers and students.
"Teachers are often relegated to course deliverers and classroom managers in the policy discussions around further education. However, it's clear that teachers have more forms of influencing inequality than is currently appreciated," said study author Dr Ben Alcott from Cambridge's Faculty of Education.
"When people speak of a positive school experience, they frequently cite a personal relationship with a teacher, and the encouragement they were given. Our research helps quantify that impact and show its significance, particularly for addressing social mobility.
"The importance of that teacher-student connection can get lost in the midst of exam statistics or heat of political debate."
Some 4,300 adolescents in England were tracked from the age of thirteen onwards, completing a detailed questionnaire every year for the next seven years. During their last year of compulsory education, the students were asked whether a teacher had encouraged them to stay on in full-time education.
Dr Alcott used mathematical modelling to "match" and compare students with similar attainment, experience and life histories -- helping control for the effects these differences had. This makes it possible for the influence of teacher encouragement alone to be measured.
"This approach brings us plausibly close to reading the long-term effect of encouragement from teachers with the data we currently have available," Alcott said.
He found that, on average across all backgrounds and abilities, rates of entry into post-16 education were eight percentage points higher in students that reported receiving encouragement (74%) over those that said they did not (66%).
Based on previous examination scores (the UK's SATs), teacher encouragement made the most difference for students with average academic achievement -- those often on the verge of going either way when it comes to further education.
For Year 11 (or 10th grade) students in the middle third of results rankings, encouragement was linked to a 10 percentage-point increase in the likelihood of university entry, yet had no observable impact on students in the upper and lower thirds.
The effect of teacher encouragement on students varied considerably depending on background -- with the greatest difference seen for students with lower levels of parental education.
For students with parents who lacked any formal qualification, post-16 education enrolment increased 12 percentage points amongst those who received teacher encouragement (64%) compared with those who didn't (52%).
This effect appeared to last into higher education, with that initial encouragement increasing the likelihood of university entry by 10 percentage points -- one-fifth higher than students from similar backgrounds who did not report being encouraged.
Students whose parents had some qualifications, but none past compulsory education, saw encouragement from teachers boost post-16 education by 13 percentage points (67% compared to 54%) and university entry by seven percentage points.
For those with parents who held university degrees, however, teacher encouragement mattered much less: increasing continued education by just six percentage points and making no difference at all to university attendance.
However, Alcott found that students from more advantaged backgrounds were likelier to report being encouraged by a teacher to stay in education.
For example, 22% of students receiving encouragement had a parent with a university degree, compared to 15% of those who did not. Similarly, students who do not report encouragement are a third more likely to have an unemployed parent (12% versus 9%).
Alcott, who formerly taught in a London academy school himself, says: "These results suggest that teachers themselves and the relationships they develop with students are real engines for social mobility.
"Many teachers take the initiative to encourage students in the hope they will progress in education long after they have left the classroom. It's important that teachers know the effect their efforts have, and the children likely to benefit most."