Background People with intellectual disabilities (ID) should be able to access the Improving Access to Psychological Therapies (IAPT) programme, currently a main provider of mainstream mental health services in England. IAPT offer cognitive behavioural therapy (CBT) to individuals experiencing mental health problems, although its effectiveness for people with ID, when delivered within IAPT, is unclear. Method Ten high‐intensity therapists took part in semi‐structured interviews, analysed using thematic analysis, regarding their experiences of delivering CBT to people with ID in IAPT. Results The rigidity of the IAPT model appears to offer a poor fit with the needs of people with ID. Therapists appeared uncertain about how to modify CBT and highlighted training and service development needs. Conclusions Findings suggest barriers to accessing IAPT largely remain unaddressed where people with ID are concerned. Services may need to reconsider what constitutes appropriate reasonable adjustments to ensure equitable access.