Yes, yes they do speak English in Hong Kong and yes you can travel to Hong Kong without learning putonghua (Mandarin) or guangzhaohua (Cantonese.) You will do just fine speaking English in Hong Kong.
I got my first hint of just how bilingual Hong Kong is on the airplane leaving San Francisco. As we headed out across the tarmac, the purser came on and gave us his usual speech. "Should Oxygen be needed, a mask will drop from the compartment over head. Please place it over your nose and mouth and tighten the straps before screaming 'Oh my God! Oh my God! We're all gonna die! If the peson next to you is screaming 'Oh my God! Oh my God! We're all going to die!' Please remember to put your mask on first before helping them." Pretty standard stuff except that when he was done, a woman came on and repeated the speech in Putonghua, then another man came on and repeated the speech in guangzhaohua.
This process repeated itself every time anything was announced for the entire thirteen hour flight. About three more times and I'd of had, "It's illegal to tamper with a lavatory smoke detector." down in all three languages.
This doubling and tripling of public announcements happens all over in Hong Kong. The re-assuring sign at the boarding dock for the cross airport subway read, "Relax, Subway come every two minutes" in about a dozen languages. Even the MTR, the regular cross town subway, repeats itself in English, Mandarin, and Cantonese.
Weirdly there is only one form of Chinese script on the signs. This is because of the weirdest fact in all of China. No matter what part of China you come from, no matter what language you speak, all Chinese people read the same alphabet. I don't get it. People who speak hokka can't speak to people who speak Guangzhohua but, if they write down what they're trying to say, any other Chinese person can read it....How this is possible, I don't know, but whatever wave of history brought written language to the Chinese did so in one fell swoop without replacing the local spoken languages. Totally blows my mind.
It's Hong Kong's amazing history that makes it such an accessible city language wise. Being a British Colony on mainland China in a part of the country where Cantonese is the local language, she just sort of grew up cattering to herself in a lot of languages. You can do pretty will with the major Indian dialects too.
For the English speaking tourist this means that the person who greets you at your hotel or restaurant is probably going to be able to speak enough English for you to order, though it can get a little rough off the main drag. We went to a couple local hangouts where the English was spotty at best. Cantonese, (guang zho hua) is the second most common language folllowed by Mandarin.
I was particularly glad that English was common on the street because it meant that I could ask random strangers where I was. My beloved map (It's in my hands in the cover photo above) served us well and true but confused me a couple of times by having the same number on different mini-maps. Where were we? Not to fear! Just ask a passing stranger. Mostly Minxi asked questions in Mandarin or Cantonese but folks often chose to answer in English. Her Cantonese is not as good as her Mandarin and sometimes our helpful friend's English proved to be the saving grace.
An American could run into a little confusion because Hong Kong speaks British English. The differences aren't that great but the subway kept warning us to be careful when "alighting" from the train. Just remember, in British English, cars have bonnets and rubbers are the pink things on the end of erasers and you'll do fine.
The one other warning on the subject of language that I would give to any Hong Kong traveler is this: All of the maps that I saw had English and Chinese street names listed but not all of the streets had English signage. The main roads seemed to be marked in English but not the side streets. Then my lack of Putonghua became clear. Several times I looked up from the map and said, "There, that sign has the square squiggly thing on it. That must be Abbot Rd."