It is not a RWY beret or badge. The badge is not RWY but it is badge no 1929 in K&K. This is an Officers cap badge for the 10th Hussars.
The Regt wore the blue beret and red backing until 1969.
This website has a good b/w photo of an Trooper with the patch.
http://www.xrhgb.com/snl09_1703_xrh.html
As an aside the RAC wore blue berets - it was only the RTC (later RTR and the RTR associated yeomanry units) who wore black ones.
Alan