This study assesses the strength of reinforced concrete beams constructed using recyclable aggregates and waste materials from medical radiology materials. The global construction sector faces significant issues about sustainability and environmental consequences that need to be resolved by adopting innovative methods for reusing materials and managing waste. On the other hand, the demolition waste produced in the construction sector can be recycled as aggregates and utilised to manufacture concrete. In this study, nine distinct trial mixes were formulated, cast, and examined, each consisting of three cubes and one cylinder. After 28 days of curing, each cube has undergone testing to determine its compressive strength. The splitting tensile strength test performed on the cylinder was utilised to assess the concrete’s indirect tensile strength. The study also explored the impact of crushed blocks as recycled aggregate at various replacement ratios of 0%, 25%, and 50%, as well as the inclusion of plastic fibre in concrete up to percentages of 0%, 0.25%, and 0.5% in volume. Utilising broken blocks as coarse aggregates in concrete will guarantee favourable economic advantages and reduced environmental impact. Plastic fibre enhances tensile strength while replacing coarse aggregate with recycled aggregate, which exhibits the opposite effect by reducing the tensile strength. Each trial mix corresponds to 1.5 m (length) × 0.1 m (width) × 0.15 m (depth) reinforced concrete beams that are cast and tested. These simple beams are directly supported and subjected to two-point loads. Furthermore, the deflection was measured by a transducer. A comparison was made between the outcome of the flexural beam test and the design strength determined according to British Standards.