Despite the stunning results, the artist's trips to London in 1900 and 1901 were marked by frustration. Monet stayed at the Savoy Hotel on the Strand and woke early each day to capture dawn over Waterloo bridge from his window. In the evening he painted the sun setting through the fog over the houses of parliament.

"Monet was fascinated by the way in which the atmosphere helped define the motif he was painting and the way the light affected the way we perceive the surroundings," said Jacob Baker at the University of Birmingham , who has carried out the analysis. "But he was under a lot of psychological stress because the weather was so changeable." Monet's letters home to his wife, Alice, bear this out: "Still no sign of the sun, nor a break in the clouds," he wrote on March 7 1900 . "Time goes by and the sun also, so that on the day when it will decide to appear, it will no longer be in the same place."

On another day he described his task as "diabolically difficult". But during those rare breaks in the gloomy British winter the results were electric. In another letter the painter told how he wanted to depict the sun "setting in an enormous ball of fire behind the parliament".

Dr Baker and his colleague John Thornes first set about establishing where Monet stood with his canvas. From the relative positions of parliament's spires and historical maps of St Thomas ' hospital, they worked out that he must have been in the administration block on the second floor - the block closest to Westminster bridge. The hospital was destroyed in the blitz.

This allowed them to work out the various potential arcs the setting sun could have followed during the days Monet was in London . As his stay wore on, the sun was setting further to the right, until eventually it was to the right of Big Ben.

The dates and times the pair report today in the Proceedings of the Royal Society, Series A, tie in with information in Monet's letters home about when he was able to paint. Dr Baker sees this as evidence that Monet's oil paintings are a true representation of the scene in front of him, so researchers could use other information in the picture as well. For example, the color of the sunset can tell scientists the size, density and composition of fog particles, with oily specks producing a yellowish green haze and soot particles giving a bluish hue.

But Christopher Riopelle, the curator of post-1800 paintings at the National Gallery in London , said he was cautious about relying too heavily on the images. "[Monet] is not taking a photograph, he is creating a surface with paint that is interesting in and of itself," he said.

"Scientific people, to my mind, often overestimate the specificity of painted images. The pictures in London one would assume would have been very accurate, but he is an artist who, in addition to observing nature, is making all kinds of aesthetic decisions." He said Monet had finished many of his London paintings when he returned to France .

Monet's second stay in London was ended by pleurisy. "Three weeks in this hotel room without being able to work," he wrote on March 29 1901 , "not having any more the heart to look at this beautiful Thames , seeing so many lost efforts."