Most of this was found on yaelf.com (young adult English as a foreign language?) and the rest on Wikipedia
1. From Dictionary of Catchphrases (1995) by Nigel Rees:
Close your eyes and think of England: Traditional advice given to women when confronted with the inevitability of sexual intercourse, or jocular encouragement to either sex about doing anything unpalatable. The source given for this phrase -- Lady Hillingdon's (or Hillingham's) Journal (1912) is suspect and has not been verified:
I am happy now that George calls on my bedchamber less frequently than of old. As it is, I now endure but two calls a week, and when I hear his steps outside my door I lie down on my bed, close my eyes, open my legs and think of England.
However, the journal has never been found and there is therefore no verification of her authorship (and, in addition, the 2nd Baron Hillingdon was called Charles!).
2. Salome Dear, Not With a Porcupine (ed. Arthur Marshall, 1982) has it instead that the newly-wed Mrs Stanley Baldwyn was supposed to have declared subsequently:
I shut my eyes tight and thought of the Empire.
3. In 1977, there was play by John Chapman and Anthony Marriott at the Apollo Theatre, London, with the title "Shut Your Eyes and Think of England".
Sometimes the phrase occurs in the form "lie back and think of England" but this probably comes from confusion with "she should lie back and enjoy it".
4. Adrian Room, in Brewer's Dictionary of Modern Phrase & Fable_(2000), writes:
Alice, Lady Hillingdon (1857-1940) married the 2nd Baron Hillingdon in 1886, but the whereabouts or even existence of her Journal is unknown.
5. The Oxford Dictionary of Quotations, Fifth Edition (1999) gives in the "Sayings and slogans" section:
Close your eyes and think of England: said to derive from a 1912 entry in the journal of Lady Hillingdon (1857-1940), but the journal has never been traced.