This study aimed to analyse public sentiments of UK-originated tweets related to COVID-19 vaccines, and it applied six chronological time periods, between January and December 2021. The dates were related to six BBC news reports about the most significant developments in the three main vaccines that were being administered in the UK at the time: Pfizer-BioNTech, Moderna, and Oxford-AstraZeneca. Each time period spanned seven days, starting from the day of the news report. The study employed the bidirectional encoder representations from transformers (BERT) model to analyse the sentiments in 4172 extracted tweets. The BERT model adopts the transformer architecture and uses masked language and next sentence prediction models. The results showed that the overall sentiments for all three vaccines were negative across all six periods, with Moderna having the least negative tweets and the highest percentage of positive tweets overall while AstraZeneca attracted the most negative tweets. However, for all the considered time periods, Period 3 (23–29 May 2021) received the least negative and the most positive tweets, following the related BBC report—’COVID: Pfizer and AstraZeneca jabs work against Indian variant’—despite reports of blood clots associated with AstraZeneca during the same time period. Time periods 5 and 6 had no breaking news related to COVID vaccines, and they reflected no significant changes. We, therefore, concluded that the BBC news reports on COVID vaccines significantly impacted public sentiments regarding the COVID-19 vaccines.