Here are a couple of tables that list the warmest and coldest 30 day spells in the Central England temperature series since 1772. So that’s a straight 30 days of daily mean temperatures that can span across one month into another. I have purposely removed any overlapping periods that occur just before and after the coldest 30 days which clutters the listing. To do this I have tried in software to identify the most extreme spell at that time and not list multiple events, which was easier said than done, here are my results using the latest available data (12 August 2019).
Warmest 30 day spell
The thirty day spell that commenced on the 22nd of June 1976 still stands out by a whisker from the 30 day spell that started on the 24th of July 1995. Both have a mean of 20.37°C so it must be the third decimal place that splits them in the sorting routine that I use. The hot spell in 2018 comes in a creditable sixth but is over a degree cooler than either the 1976 or 1995 spell.
Coldest 30 day spell
The coldest 30 day spell was the one that started just after Christmas on the 28th of December 1813 with a mean of -3.33°C and Charles Dickens would have still been a year old. The same start and dates in the year 1962/63 produced a mean of -2.71°C, I notice that severe winter of managed two distinct entries in the top forty coldest spells. In recent years only spell in 2009 and 2010 managed to make it to the top forty, 39th and 13th respectively.