Yes in the North East.
We have a road circuit and Velodrome locally and a couple more not far away which has youth training from 2 local clubs on evenings and weekend and specific kids skills and racing event 12 times a year on an evening. Basically from being able to use a pedal bike so 3+
Plenty of other youth racing down to U8 around the area. Not so much for U6 but they don’t need more yet.
The local MTB club do evening rides/training but is aimed at about 10 upwards really. There is one U8 who goes but he’s strong.
Club in Scarborough also run a fair few grass based MTB races but not made it to any this year.
York has a pretty active Velodrome and circuit also.
Not sure what the age limit on the velodrome is but fixed might be interesting if you chuck some 6 yo on :0)