Supporting more autistic people into employment is a major priority of the United Kingdom's National Autism Strategy (2021-2026). However, little is known about the barriers employers perceive to hiring autistic people. A pre-registered cross-sectional survey study was conducted on a nationally representative sample of 1212 individuals with recent hiring experience. The Capability, Opportunity, Motivation -- Behaviour framework and the Theoretical Domains Framework were used to identify perceived barriers to hiring autistic people. Results indicated that intentions to hire autistic people and to make adjustments to the hiring process were high. However, barriers existed in relation to knowledge about autism and how to make adjustments, as well as perceived limited opportunities to hire autistic people. Intentions to hire autistic people were higher for younger participants, men, people with higher levels of autism knowledge and those with more experience of previously hiring autistic people. Analysis of qualitative responses revealed employer concerns about workplace relationships, productivity and the need for training and adjustments to hiring processes. This study demonstrated that important targets for intervention are improving employer knowledge of autism and building more inclusive hiring practices. Practical suggestions for implementation are provided. These findings are significant for development of policies aimed at improving employment outcomes for autistic people.