Despite large language models (LLMs) being known to exhibit bias against non-standard language varieties, there are no known labelled datasets for sentiment analysis of English. To address this gap, we introduce BESSTIE, a benchmark for sentiment and sarcasm classification for three varieties of English: Australian (en-AU), Indian (en-IN), and British (en-UK). We collect datasets for these language varieties using two methods: location-based for Google Places reviews, and topic-based filtering for Reddit comments. To assess whether the dataset accurately represents these varieties, we conduct two validation steps: (a) manual annotation of language varieties and (b) automatic language variety prediction. Native speakers of the language varieties manually annotate the datasets with sentiment and sarcasm labels. We perform an additional annotation exercise to validate the reliance of the annotated labels. Subsequently, we fine-tune nine LLMs (representing a range of encoder/decoder and mono/multilingual models) on these datasets, and evaluate their performance on the two tasks. Our results show that the models consistently perform better on inner-circle varieties (i.e., en-AU and en-UK), in comparison with en-IN, particularly for sarcasm classification. We also report challenges in cross-variety generalisation, highlighting the need for language variety-specific datasets such as ours. BESSTIE promises to be a useful evaluative benchmark for future research in equitable LLMs, specifically in terms of language varieties. The BESSTIE dataset is publicly available at: https://huggingface.co/ datasets/unswnlporg/BESSTIE.