The findings come from the Avoid programme, run by the Met Office in conjunction with other UK research institutions under government funding.
The latest results were presented at the UN climate summit in Copenhagen.
The Avoid programme aims to use the latest scientific understanding to make risk-based assessments of the impacts, global and regional, of rising greenhouse gas emissions.
'Virtually impossible'
Echoing the general conclusion of other analyses, including by the Intergovernmental Panel on Climate Change (IPCC), the Avoid researchers conclude that the earlier global emissions peak and begin to decline, then the gentler that decline can be.
So peaking in 2018 and shrinking emissions by 4% per year after that would give a 50% chance of keeping warming below 2C, it calculates.
But if the peak came just two years later, in 2020, the decline would then have to be 5% per year for the same odds of staying below 2C.
"If you go to 2025 before peaking, it's virtually impossible to stay under 2C," said Vicky Pope, head of climate science at the Met Office.
Drawing on socio-economic research from other institutions in the project, the Avoid team believes that cutting emissions by more than 5% per year would be the maximum feasible.
'Negative emissions'
A bloc of small island states and vulnerable African countries are demanding that any new deal on climate change should aim to keep the temperature rise below 1.5C.
But the Met Office analysis suggests that would be very difficult.
"There's no way you'd get a 50% chance of avoiding 1.5C," Ms Pope told BBC News.
"If you reduced everything to zero immediately you'd still get about 1.3C because of the greenhouse gases already in the atmosphere."
Policies to ensure a reasonable chance of remaining under 1.5C would involve "negative emissions" - sucking CO2 out of the air - she said.
And if emissions peak later than 2020, negative emissions - a form of geo-engineering - would be needed even to hit the G8's 2C target.
The concept of geo-engineering has its adherents but it is also fraught with economic, social and technical difficulties.
A report by the UK's Royal Society, released in September, concluded that although the approach might have a role, there were "major uncertainties regarding its effectiveness, costs and environmental impacts", and was no substitute for curbing emissions.
It was announced on Thursday that more than 1,700 scientists had signed a statement to defend climate science.
The response has been co-ordinated by the Met Office in the wake of the "ClimateGate" row.
The scientists became concerned after climate change "sceptics" claimed e-mails taken from servers at the University of East Anglia's Climatic Research Unit (CRU) suggested researchers had manipulated evidence.
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If you go to 2025 before peaking, it's virtually impossible to stay under 2C
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