Driver Monitoring Systems (DMS) in Conditionally Automated Vehicles (CAVs) can identify if the driver has an appropriate state of awareness to be taking control of the driving, if the vehicle requires them to do so, and then indicate this to the driver through Human Machine Interface (HMI). This has the potential to improve road safety by eliminating accidents caused by human error during transition of driving control between the vehicle and driver due to distraction, fatigue, and other undesirable driver states. However, the potential benefits and utility that these technologies can provide may be overlooked due to a lack of trust, which affects their acceptability. To explore current perceptions that affect the acceptability of DMS and HMIs in CAVs, a scenario-based survey that combines the Car Technology Acceptance Model (CTAM) with qualitative questions exploring the changes to technology that may increase its social desirability, was conducted with 63 respondents (32 females, 33 males). The data was compared against demographic characteristics of age, gender, frequency of driving and duration of holding a license. The quantitative results indicated that gender has a significant effect (p = 0.043) on anxiety experienced towards technology. The qualitative findings showed that the respondents would like to have more information about the working of the technology, including system states, provided through training, videos or other support suggesting a current lack of understanding of how such technologies work. The study offers some takeaways to vehicle manufacturers, related other equipment manufacturers and policymakers on the design and implementation of such technologies to increase acceptability.