Compulsory wearing of cycle helmets

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I would like to make wearing cycle helmets compulsory.  On May 28th my Mum was knocked off her bike and died instantly when her head hit the road.  She had been a cyclist for nearly 70 years, her bike being her only mode of transport. She did not wear a helmet, because she never had and was only coming back from the Co-op.  I went to the scene and saw my Mum lying on the road, the blood, her possessions scattered on the far side of the road.  I have been reading about how cyclists allegedly become more reckless if they wear a helmet, how drivers are not so careful when overtaking them if they have a helmet on, how roads should be better designed and there should be more cycle lanes.  But none of this would have saved my Mum right at this moment in time- but a helmet might have.  We all know too that any measures that might be taken by the Government etc to make the roads safer will probably never happen. Furthermore, if all these arguments about not wearing helmets are correct, why then are motorcyclists legally compelled to wear a helmet?