In this paper, we introduce a new English Twitter-based dataset for cyberbullying detection and online abuse. Comprising 62,587 tweets, this dataset was sourced from Twitter using specific query terms designed to retrieve tweets with high probabilities of various forms of bullying and offensive content, including insult, trolling, profanity, sarcasm, threat, porn and exclusion. We recruited a pool of 17 annotators to perform fine-grained annotation on the dataset with each tweet annotated by three annotators. All our annotators are high school educated and frequent users of social media. Inter-rater agreement for the dataset as measured by Krippendorff's Alpha is 0.67. Analysis performed on the dataset confirmed common cyberbullying themes reported by other studies and revealed interesting relationships between the classes. The dataset was used to train a number of transformer-based deep learning models returning impressive results.