Some tracks will allow an open face helmet, you'd need to check with the individual track tho, usually at Regional/National level they would LIKE a full face helmet to be worn although not a dfinitive rule.
TBH you can get some really good quality full faces at reasonable prices, FLY and 661 both do models from £50 upwards, after knocking 4 teeth out wearing an open face and mouthtrap i prefer me full face lid nowadays