You can definitely get by in Cayo even if you just speak English. You do not need to speak Spanish because about 90% of the people here in Cayo can understand English. Only some of the older folks in the small villages might not be able to speak English.
English is taught in school so all the kids and younger people speak English. It is an advantage if you speak Spanish though. It is a psychological thing because that way you can approach people in their mother language. Although Belize is an English-speaking country, 80% of the people in the villages still speak Spanish as well.
All legal dealings such as contracts are in English in Belize. If you need to get your water in your house turned on or if you need to go to a government office, the language they use in their offices is English. They speak American type English here.
Creole is another important language that is spoken in Belize along with Spanish and English. Creole is derived from English but don’t think that just because you speak English, you could also understand Creole. You might understand some of it immediately because some words are similar to English but as they speak fast you will not be able to follow.
Belizeans are tolerant to different cultures and different accents and language in general because there are so many people from different places living here. They know that nobody is perfect and everybody will speak a little different. So if you have a British accent, they will try to understand you. If you are from Texas, they will adjust to your accent as well. If you do not understand them the first time, they will repeat it for you. Belizeans always try their best to please the visitors in their country. They are innately friendly and that is a big factor in communication.
Generally, if you only speak English, you can get by in Belize perfectly. This is one of the advantages of Belize over other Caribbean countries. My wife and I do not speak Spanish and we never had an issue.
(Pictured: large carved fish being moved by a Belizean with a t-shirt in English, to Vanilla Hills Lodge, Cayo, Belize.)