This study aimed to explore the impact of carer stressors (neuropsychiatric symptoms of dementia, level of independence in activities of daily living, hours of caring per week), demographic factors (carer age, relationship with the person with dementia, dementia type, dementia severity, number of years since diagnosis and cohabitation status) and psychological inflexibility on depression and anxiety in family carers of people with dementia. Eighty-nine family carers with a mean age of 69.13 years old completed self-reported and interview-based questionnaires. Participants were primarily female family members aged 65 years or older looking after a person with severe Alzheimer's disease. Two final regression models (Depression model R2 = 0.43; Anxiety model R2 = 0.43) demonstrated that psychological inflexibility (β = 0.52) and the number of hours devoted to caregiving (β = 0.23) had a significant impact on carer depression, while psychological inflexibility was the only significant independent predictor of carer anxiety (β = 0.55). The findings demonstrated psychological inflexibility to be a common factor explaining mental health problems in this population even after controlling for other variables known to have an impact. Acceptance and Commitment Therapy (ACT) may be beneficial for concomitantly treating depression and anxiety in this population. Considering that fifty-two per cent of participants responded that they devote more than 41 h to caregiving per week, a non-traditional face to face approach such as online ACT may have potential in future research. Future studies should also explore the suggested models in understudied subgroups of carers (e.g., carers of early-onset dementia, carers of people with early-stage dementia).