I might be going to a 3 week camp (it's not really a camp, it's more of an academic program) in Hong Kong. How many people (a lot, a few, only certain occupations, etc.) speak English, and do they speak Mandarin too? I don't know Cantonese.
As a foreigner residing in Hong Kong, I would actually advise you not to worry about the language since majority of the people speak English. You will not have any communication problems unless you visit a few remote areas or when you deal with Mainland Chinese tourists and a few locals who do not speak English (Some of them speak English too).
I would suggest you taking the advices from Wikitravel.
Nevertheless, most locals under the age of 40 (and many over that as well) know enough English for basic communication. To improve your chances of being understood, speak slowly, stick to basic words and sentences, and avoid using slang.
You may also speak Mandarin, which is also widely understood in the city.
I spent my semester abroad in Hong Kong (at HKUST) last year. Basically everybody speaks English, from taxi drivers to cashiers. Also road signs etc. are all in English as well.
The students at HKUST did understand Mandarin, but were quite reluctant to speak with you in Mandarin, they definitely prefer English.
I do not read Chinese very well and speak only at a conversational level, but I have never had problems in Hong Kong, even ignoring my ability to speak some Cantonese.
Perhaps you already know this, but many public spaces (street signs, the bus or the metro, etc.) are bilingual. So are many "menus" at many "fast-food" chains I have seen. (To boot, I remember someone at a Subway being only able to speak in English to me.) Between this and some level of competency in basic English among cashiers / servers / etc., I don't see much potential for a complete inability for someone who does not speak Cantonese to get by. (This has been alluded to in other answers.)
Since Mandarin, in addition to English, is taught in schools, some people may also speak it. However, it's not unlikely for someone's Mandarin pronunciation to be rather bad, and there may be some overlap between who speaks Mandarin and who speaks English. Moreover, at least among some segments of the population (e.g. those who have spent a lot of time abroad in Anglophone countries, or some segments of the wealthier, which may include academic types), English may be a much safer bet than Mandarin. This may even still be true for other groups, such as the "average" student (as stated here): I know of people who grew up in the public school system in Hong Kong who are much more comfortable speaking English than speaking Mandarin.
I was there from 19th to 23rd, and most people of working age and of the white-collar occupations speak English. However, you might want to have an extra patience on listening and understanding them as their Chinese accent indeed has bearing on their pronunciation.
Locals farther away from Central (e.g. Shau Kei Wan) tend to be less knowledgeable in English.
With the influx of mainland Chinese and the Return (internationally "Handover") of HK to China, Mandarin slowly creeps in. However, due to various reasons while many Hongkongers speak Mandarin, they tend to favor Cantonese.
I'm now traveling in Hong Kong and have talked with at least 120+ people, including airport, cafe, restaurants, police, hotel, bank, shop clerks, station attendants, money exchanger, etc... but only 5 people cannot speak English, one of them is a security guard (age 50s or 60s men), another one is a beggar (60s men I think), another one is a cleaning staff at hotel (maybe 40s women), and the other two are staff at cafe and convenience store (40s or 50s women).
It seems to me that most people who is either under 40 to 45 or white-collar have little or no problem in speaking English. The elderly people are far more likely to be unable to speak English.
I can even assume that I won't have any problems to live in Hong Kong without learning Chinese (Cantonese).
Also note that I travel around Hong Kong Island; maybe less peoples can speak English in Kowloon.