Anaesthesia, the publication of the AAGBI, has a digital archive dating back to 1946 which is only accessible to members through their site. However it does appear that the journal is is searchable at this link and some articles, like case reports, are free. 

Anaesthesia and Intensive Care has an archive back to 1972. It can be searched and occasionally some history articles are free, but most require a log-in

British Journal of Anaesthesia has an archive back to 1923 which can be freely searched but requires a log-in to access the articles

The Lancet archive dates from 1820 

The Times newspaper archive dates from 1785