Hawking graduates from Oxford before moving on to Cambridge University to study cosmology and general relativity. He begins to take serious notice of his deteriorating motor abilities during this year and is persuaded by his mother to undergo medical tests. From his memoir, My Brief History:
In my last year at Oxford I noticed that I was getting increasingly clumsy. I went to the doctor after falling down some stairs, but all he said was “Lay off the beer.” I became even more clumsy after moving to Cambridge. At Christmas, when I went skating on the lake at St. Albans, I fell over and couldn’t get up. My mother noticed these problems and took me to the family doctor.