Carbon emissions have risen at most of the UK's universities over the past five years, a new league table published by the Guardian reveals, prompting concern that institutions will fail to meet strict targets for reductions by 2020.

Nottingham Trent University topped People & Planet's annual Green League, closely followed by Gloucestershire, Worcester and Plymouth – but elite universities were left trailing.

Overall, carbon emissions at 139 universities rose by 3.9% between 2005 and 2010, even though capital funding for English institutions is now linked to reductions.

People & Planet said the results were "incredibly worrying" and suggested that, unless there is a rapid turnaround, the sector would not achieve its commitment to cut emissions by 43% by 2020. The average increase across universities was 7.4%, with rises of more than 50% recorded at nine institutions, the research shows.

While newer, teaching-focused institutions did well, carbon emissions rose at three-quarters of the 20 members of the research-intensive Russell group. The highest-placed member of the group was the London School of Economics, at number 22, earning it a "first" in the table's degree classification style.

Only five Russell group institutions got 2:1s, 10 received 2:2s, and three – Oxford, Sheffield and Liverpool – managed only thirds. Cardiff, at number 130, was deemed to have "failed". Oxford was in 103rd place and Cambridge came 68th.

According to milestones set in the higher education sector's carbon reduction strategy, a maximum increase in emissions between 2005 and 2012 of 1% would be allowable to keep it on track to meet the 2020 target.

People & Planet's climate campaigns and communications manager, Louise Hazan, said: "The planning is there, the policy is there, to a certain extent the resourcing is there, but the performance is just lagging behind. On current trends the sector is nowhere near reaching the emissions cuts required of all public sectors by the Climate Change Act."

She added: "There's been no high-level acknowledgement of the importance of this … for [universities minister] David Willetts, in particular, the recommendation is clear: show more leadership and vision for a sector-wide, low-carbon transition plan within the next 10 years and prioritise the resources to help universities achieve it."

Andrew Smith, head of estates and sustainable development at the Higher Education Funding Council for England (Hefce), said: "This is a really pressing issue. We've got a load of plans and strategies; what we really need now is delivery."

A spokeswoman for the Department for Business, Innovation and Skills said: "Even in fiscally challenging times, the government remains committed to achieving the targets for carbon reduction and making progress on the wider sustainable development agenda".