Green’s Dictionary of Slang

1. to drive very fast and without noticing anyone else on the road.

1923

Daily Mail 21 June 12: Motor-cyclists who blind along the road .

2. in fig. use, to rush headlong into.

1935		Punch 21 Aug. 198/1: It is far better to get a little work done which is perfectly planned and organised than to let people go blinding on without anyone in authority knowing what they are doing [OED].
1954		C. Fry Dark is Light Enough 78: A trap, they’ve set for us. Who’s got our pistols? Gone blinding into it.