Social media platforms such as Twitter (currently X) have become important sites of public discourse and participation. Researchers have attempted to identify and collect Twitter data within a certain country or region in order to answer research questions within a particular locale. However, location information of tweets is limited. Tackling the case of public blaming of minorities on Twitter in the context of the COVID-19 pandemic in the UK, we present a method for identifying UK-based tweets and analyse two types of datasets that we collected and processed: (a) tweets with UK location-tags (labelled as location-specific data and referred to as UK datasets); and (b) tweets with UK location-tags and / or user profiles containing potential UK location information (labelled as location-open data and referred to as ALL datasets). The empirical results reveal that the overall sentiments in the two dataset types align in the same direction, but the location-specific datasets contain more extreme discourses (i.e., more positive and more negative sentiments and fewer neutral sentiments). Furthermore, in the location-specific datasets, the range of theme areas is narrower, although the themes still grasp the essence of the discussion about blaming minorities found in the larger dataset. The findings demonstrate strengths and limitations of the two dataset types and that the location-specific data can be suitable especially when the available research resources are insufficient for collecting or processing larger datasets. Nevertheless, we propose that future research may consider comparing smaller and bigger datasets to test differences between these for other topics for which specific locations may be of particular interest.