Looking over the Sport England list of recognized sports I cannot see any reference to RC or the BRCA mentioned as a National Governing Body. (as a btb, model aircraft flying is recognized as a sport).
Lists
HERE and
HERE
EDIT 19th November 2018 : (Application Granted 15th November.)
I asked (today) the BRCA if they were on the list 'Sporting Activities and Governing Bodies Recognised by the Sports Councils'
from Sport England web site.
The nice quick reply from the BRCA is, 'You'll find Motor Sport and the MSA (Motor Sport association now operating as 'Motorsport UK') on the Sport England list.'
A search on the motor sport association website will find the BRCA