Intelligent Transportation Systems (ITSs) require ultra-low end-to-end delays and multi-gigabit-per-second data transmission. Millimetre Waves (mmWaves) communications can fulfil these requirements. However, the increased mobility of Connected and Autonomous Vehicles (CAVs), requires frequent beamforming - thus introducing increased overhead. In this paper, a new beamforming algorithm is proposed able to achieve overhead-free beamforming training. Leveraging from the CAVs sensory data, broadcast with Dedicated Short Range Communications (DSRC) beacons, the position and the motion of a CAV can be estimated and beamform accordingly. To minimise the position errors, an analysis of the distinct error components was presented. The network performance is further enhanced by adapting the antenna beamwidth with respect to the position error. Our algorithm outperforms the legacy IEEE 802.11ad approach proving it a viable solution for the future ITS applications and services. ; Comment: Proc. of IET Colloquium on Antennas, Propagation & RF Technology for Transport and Autonomous Platforms, to appear