So, by example, if the Quarantine Specialist is in London, and an Epidemic card is pulled and the affected city is New York (or another connected city), does the specialist cancel the placement of infection cubes in New York?
Yes, she cancels the placement of any disease cubes on a city she is in and connected cities.
Note that this does not "prevent the Epidemic"... when an epidemic card is drawn, you still fully deal with it. It's just that during the "infect" step of the epidemic, she can prevent the extra infection.
From the rules:
The Quarantine Specialist prevents both outbreaks and the placement of disease cubes in the city she is in and all cities connected to that city. She does not affect cubes placed during setup.