Much as I detest the DM, the only way to get a good outcome here is either to make it irrelevant or to find a way to get it onside. Perhaps if the "strict liability" campaigns were to concentrate on pedestrians and how this would help them defend against pavement cyclists and suchlike, the Wail would support them as an anti-cyclist measure?
The problem is that cycling is associated with 'the left' what with the whole being green and not showing off how wealthy you are with a flashy motor, and thus - like issues such as climate change, which the Daily Mail also associate with the left - they will always be hostile towards it.