Research has reported the benefits of companion animals for people with severe mental illness (SMI). However, this evidence base is fragmented and unclear. The COVID-19 pandemic presents an opportunity to explore the role of companion animals in the context of social distancing and isolation measures for people with SMI. Therefore, we aimed to investigate the links between mental and physical health and animal ownership in people with SMI and to explore animal owners’ perceptions related to human–animal interactions during the pandemic restrictions. A survey was conducted with a previously assembled cohort of individuals with SMI in the UK. The survey included previously validated and new bespoke items measuring demographics, and outcomes related to mental and physical health, and human–animal interactions. The survey also included a question inviting free-text responses, allowing participants to describe any experiences of their human–animal relationships during the pandemic. Of 315 participants who consented to participate, 249 (79%) completed the survey. Of these, 115 (46.2%) had at least one companion animal. Regression analyses indicated that animal ownership was not significantly associated with well-being and loneliness. However, animal ownership was associated with a self-reported decline in mental health (b = 0.640, 95% CI [0.102–1.231], p = 0.025), but no self-reported change in physical health. Thematic analysis identified two main themes relating to the positive and negative impact of animal ownership during pandemic restrictions. Animal ownership appeared to be linked to self-reported mental health decline in people with SMI during the second wave of the pandemic in the UK. However, the thematic analysis also highlighted the perceived benefit of animal ownership during this time. Further targeted investigation of the role of human–animal relationships and the perceived human–animal bond for human health is warranted.