I had an identical encounter as you daftgrandad a couple of years ago and it was on an almost deserted road and I refused to let her past (probably a different story if it had been a 6' bloke).
Most annoying is one local road where there are wide cycle lanes on both sides and yet, so often, there are cyclists on the pavement on the side where the traffic is moving in the same direction in which they are travelling, so that the cyclist only has to move a yard to their right to be in the cycle lane.