Also, Cook is just 40 runs shy of Gooch's England record of 8900 test runs. We will shortly have England's leading run-scorer and wicket-taker playing in the same team as record holders. I was trying to work out when the last time that would have happened is. I thought it would be an easy exercise, turns out it isn't...
I thought it would be early 90's, when Gower/Gooch and Botham were all nearing the end of their careers, but it turns out that Gower broke Boycott's England scoring record the match after Beefy retired (
http://www.espncricinfo.com/ci/engine/match/63577.html).
Then I went back to Boycott and Bob Willis, both previous record holders, but no, Willis didn't pass Trueman's record until Jan 1984, a couple of years after Boycott retired.
Prior to that the record holders were Colin Cowdry and Fred Trueman, but their periods of being record holders never overlapped either.
Prior to that the runs record holder was Wally Hammond, who finished his career in 1947. For the length of his career, the England record for wickets was held by Sid Barnes. Obviously they never overlapped either.
So I think the answer is Sid Barnes' final test match, the 4th test between England and South Africa at Durban, February 1914.
http://www.espncricinfo.com/ci/engine/match/62519.html, when the England runs record holder was Sir Jack Hobbs, who at the time had around 2400 (and would go on to retire with over 5000, 16 years later)