http://www.weatherca...es_changes.html, which mentions a daily range of 24.0 deg. C. from 4.3 deg. C. to 28.3 deg. C. at Chesham, Buckinghamshire, on 23rd May 2010, also states that the highest daily range in Britain is from Altnaharra in Sutherland where the range was 29.3C on 30th December 1995. This would imply a range from -27.2 deg. C. to +2.1 deg. C.
http://www.personal....in_december.htm states that the range on 30.12.1995 was from -27.2 deg. C. to +1.7 deg. C.
Strictly speaking, although no doubt it was within a 24 hour period, the -27.2 deg. C. and the +1.7 deg. C. (or +2.1 deg. C.)were within different 0900 to 0900 GMT periods (this of course also presumably applies to the Tummel Bridge range of +29.0 deg. C. from -7.0 deg. c. to +22.0 deg. C. on 9th May 1978 and the range of 28.3 deg. C. from +1.1 deg. C. to +29.4 deg. C. at Rickmansworth on 29th August 1936, so strictly one should only consider ranges where there has been a considerable drop from one afternoon through the following evening and night, and although this is probably too purist for most, it is to me equivalent to the difference between the wettest 0900 to 0900 GMT period in Britain (279 mm at Martinstown, Dorset, on 18th/19th July 1955) compared with the 316.4 mm which fell at Seathwaite in Cumbria in a non-standard 24 hour period around 19th and 20th November 2009 (see
http://www.personal....in_november.htm, 142.6 mm falling in the 24 hours from 0900 GMT on 18th to 0900 GMT on 19th, and 246.6 mm falling in the 24 hours from 0900 GMT on 19th to 0900 GMT on 20th.
I think in the British climate, the fall in temperature would not be as much as the potential rise in temperature, as it often takes several days to reach an extremely low mininimum in winter, e.g. when there is a heavy snowfall, followed by several calm clear nights; at other times of year snow is much less likely. In the case of Rickmansworth in August 1936, I think the succeeding night fell to about 40 deg. F. or c. 4.4 deg. C., still giving a large daily range of about 25.0 deg. C. However the largest daily range in the world, of 100 deg. F. (c. 55.6 deg. C.) from +44 deg. F. (c. 6.7 deg. C.) to -56 deg. F. (c. -48.9 deg. C.) at Browning, Montana, U.S.A., from 23rd to 24th January 1916 - see
http://en.wikipedia....Montana#Climate (although this only states that it is the USA's, not the world's, greatest daily range).