With the climate crisis and pursuit of efforts to reduce embodied carbon impacts in the built environment, steel-timber hybrid structures have emerged as a sustainable form of framed construction which offer numerous benefits over the widely used and well-established steel-concrete hybrid structures. However, there are major concerns about the structural fire performance of such systems among various stakeholders in the construction industry, particularly for the design implications in terms of the lateral-torsional buckling behaviour and the degree of lateral restraint mobilised in the steel-to-timber connections. The screws that connect cross-laminated timber slabs to steel beams may provide a certain degree of restraining action in fire. However, further investigations are required to quantify the slip characteristics of such connections. In this study, it was found from existing literature that at the fire limit state, the continuous elastic lateral stiffness available to restrain the beam varies between approximately 500 kN/m/m and 2000 kN/m/m. Relying entirely on the screws and using this practical range of stiffness, a parametric study using Eurocode 3 design buckling resistance equations on 9 m simply supported span steel beams and beam-columns with span-to-depth ratios of about 10, 15, 20 and 25 was performed. The results indicate that designing such members as fully restrained in fire conditions may lead to unrealistic assumptions and unsafe structures.