The metaphorical framing of refugees, asylum seekers, and immigrants (RASIM) has been widely explored in academia, but mainly through close analysis. The present research outlines a large-scale computational investigation of RASIM metaphors in UKs media discourse. We experiment with a method that facilitates automatic identification of RASIM metaphors in 21 years of RASIM-related news reports from eight popular UK newspapers. From the metaphors extracted, four overarching frames are identified. Further analysis reveals correlations between political bias and metaphor usage: overall, right-biased newspapers use RASIM metaphors more frequently than their left-biased counterparts. Within the metaphorical frames, water, disaster, and non-human metaphors are more prevalent in right-biased media. Additionally, diachronic analysis illustrates that the distinctions between left and right media have evolved over time. Water metaphors, for example, have become increasingly more representative of the political right in the past two decades.