(1) Background: Patients with dysphagia are at increased risk of stroke-associated pneumonia. There is wide variation in the way patients are screened and assessed. The aim of this study is to explore staff opinions about current practice of dysphagia screening, assessment and clinical management in acute phase stroke. (2) Methods: Fifteen interviews were conducted in five English National Health Service hospitals. Hospitals were selected based on size and performance against national targets for dysphagia screening and assessment, and prevalence of stroke-associated pneumonia. Participants were purposefully recruited to reflect a range of healthcare professions. Data were analysed using a six-stage thematic process. (3) Results: Three meta themes were identified: delays in care, lack of standardisation and variability in resources. Patient, staff, and service factors that contribute to delays in dysphagia screening, assessment by a speech and language therapist, and delays in nasogastric tube feeding were identified. These included admission route, perceived lack of ownership for screening patients, prioritisation of assessments and staff resources. There was a lack of standardisation of dysphagia screening protocols and oral care. There was variability in staff competences and resources to assess patients, types of medical interventions, and care processes. (4) Conclusion: There is a lack of standardisation in the way patients are assessed for dysphagia and variation in practice relating to staff competences, resources and care processes between hospitals. A range of patient, staff and service factors have the potential to impact on stroke patients being assessed within the recommended national guidelines.