Thank you both for the feedback. The lawn areas I mow are flat but are connected by a concrete path with a left hand elbow half way down.
I have thought of adding additional weight to increase traction but I think that would be difficult practically. The mower has a catcher at the rear and limited area to add weight. Due to the profile of the path and rigidity of the mower frame, I think it would require a great deal of weight to force the right rear wheel to gain traction in the section where it loses traction. I have tried moving the mower seat as far back as possible, but it seems to have no effect. Have tried different concrete coatings to improve grip but again the wheel just skids lightly over the top of it in this section.
I am attracted to the idea of additional braking. I think(?) I read somewhere where some add front brakes to Go Karts? Even if I operated the additional braking manually, I think it would be a big improvement in safety.
It surprises me that ride-ons can be sold with potentially so little braking? The cause is explained here where diff lock is not engaged (or the mower does not have diff lock)
If push bikes come with front and rear brakes, then I don't think it is overkill to extend a ride-ons braking from potentially one wheel (or less), by fitting additional braking. Finding someone to do it might be the problem.