As someone who kind of remembers 73 in England, the coffee is way better now. Also we had some epic strikes and power cuts back then and a splendid 73% market crash. After decades of relative economic decline we decided to join EEC, the predecessor to the EU after which things recovered economically from the 'sick man or Europe' to the fastest growing economy in Europe until we recently voted to go back to the good old days.
Only joining the EEC had little, if anything, to do with the recovery and change of coffee.
You remember a country still suffering from WWII and loss of world leader role (and colonies), in a much poorer global period. For starters, the '70s had a global recession and oil crisis, and many countries were affected, not just England. Have a look at pictures of New York of the same period -- it looks like a third world country [1].
In the 80s and 90s, countries that didn't join the EEC, as well as countries that joined EU much later, had the same economic uplift.
(And of course several countries that did join the ECC/EU had economic decline and crashes, e.g. the P.I.I.G.S).
Yeah there were many factors. The UK used to be quite socialist in the 1945-1975 period which was OK for the NHS but many other things like British Leyland didn't work so well.