Cambridge University has launched a £500m fundraising campaign to pay for a new “transition programme” to encourage and support applications from talented students from disadvantaged backgrounds who might otherwise not get a place.

The scheme will include an intensive three-week bridging programme plus an additional transition year before a degree, to raise the attainment of disadvantaged students who have academic potential but may fall short of high entry requirements.

It comes as pressure mounts on leading universities, especially Oxford and Cambridge, which are still dominated by white, wealthy students, many of whom are privately educated, to widen access to those from traditionally underrepresented backgrounds.

Figures published in June showed some Cambridge colleges admitted no black students or accepted as few as one a year between 2012 and 2016. In August, the grime artist Stormzy said he would fund two scholarships for black British students to go to Cambridge.

Giving the traditional start-of-year speech to university staff on Monday, Cambridge’s vice-chancellor, Prof Stephen Toope, said: “Can we call ourselves a place of excellence if we are not fully inclusive of the most diverse talent? This is not just a matter of box ticking.

“For Cambridge, this is an ethical issue. We can only expect to have full public support for our university if we are prepared to encourage top talent to pour in – regardless of where it flows from.”

He insisted the university would not lower admission standards, but encouraged applications from undergraduates and postgraduates in the the UK and overseas who may have been disadvantaged as a result of their educational journey.

He also said Cambridge could not class itself as a “truly great” university if it was not open to social and cultural diversity. “It falls on us to dispel the facile stereotypes of Cambridge as a bastion of privilege and self-serving elitism,” he said.

The scheme follows a similar initiative at Oxford University’s Lady Margaret Hall, headed by the former Guardian editor-in-chief Alan Rusbridger, which in turn was based on a programme used by Trinity College Dublin.

Cambridge was unable to offer any detail on how many disadvantaged students might be supported, because of the current uncertainty in the sector pending the outcome of the government’s post-18 education review by Philip Augar, but the £500m will also go towards other forms of student support including mental health help for students facing difficulties.

Lee Elliot Major, the chief executive of the Sutton Trust, which promotes social mobility through education, said: “Young people from low-income homes are seriously underrepresented at top universities and we will need radical change to shift this.

“A new transition programme for low-income students could do much to widen participation and provide additional support for those students who need it most. But it will be important that Cambridge invests in careful and robust evaluation to make sure it is implemented in the most effective way.”