The source of that FT chart refers to Harry Kennard who I googled.
From a section of his blog (
statistics – Harry Kennard), there is a link to an ONS page with daily deaths in England and Wales from 1970 to 2014. That peak in January is January 1970.
The peak weeks (using Saturday to Friday as a week as they did for the recent reporting) were the week 1 January 1970 (20,444), week 51 December 1989 (18,791), week 1 January 2000 (18,731). Week 50 December 1989 also had over 18,000 deaths reported with 18,258. Highest death total for a day in that period is 2 January 1970 with 3,255 deaths reported.
The blog also refers to another ONS page with an article on excess winter deaths since 1950/51 where you can download the data (not weekly figures) from 1950/51 to 2015/16.
Excess winter mortality in England and Wales, by region, sex, age group and local authority.
www.ons.gov.uk