'Cycling Solicitor' no.1 describes this as a 'traffic calming measure'. If that is what it is claimed to be, then it is a 'road hump' as defined in s.90F of the Highways Act 1980. The Highways (Road Humps) Regulations (link below) sets out requirements for road humps at section 4:
"
no road hump shall be constructed or maintained in a highway unless - ... (d) no vertical face of any material forming part of that road hump exceeds 6 millimetres measured vertically from top to bottom of that face.
From the photo you took, it's clear that the vertical face is more than 6mm high. This then shows negligence in installing traffic calming measures which do not conform to prescribed requirements. That gives grounds for an action in negligence.
I doubt this was introduced as traffic calming measure. It appears that this is simply poor workmanship and failure to properly check and supervise the work done to ensure that this met safety requirements. i.e. the work was done negligently.
You would also have grounds for an action for damages in public nuisance as well. (This hazard in the highway is a public nuisance and you suffered damage because of it. Highway Authority would have to show they have statutory power to put this kind of step in the road. They might possibly find that - in section 77 of the Highways Act 1980:
(1)Without prejudice to section 76 above, a highway authority may raise or lower or otherwise alter, as they think fit, the level of a highway maintainable at the public expense by them.
(2)A highway authority shall pay compensation to any person who sustains damage by reason of the execution by them of works under this section.
I recently tried to find if there had been any cases reported on s.77 claims, but couldn't find anything. I'm not sure if it is applicable - I think it may be more for where a highway is raised or lowered blocking views etc. (at least that is what can be gathered from Parliamentary debate about this). If properly interpreted, this wouldn't give a Highway Authority power to put in safety hazards in the road like this. (that interpretation would make a nonsense of other legislation - such as road humps regulations).
An action in negligence is clearer and probably simpler. But if they want to claim authority under s.77(1), you can claim damage under s.77(2).
The possible area of difficulty you may have is proving that you had the accident (were there witnesses?). You would have to show 'on balance of probabilities' that the accident happened and was caused by this defect.
Road Hump Regulations:
http://www.legislation.gov.uk/uksi/1999/1025/pdfs/uksi_19991025_en.pdf
BTW - I think you are better without 'Cycling Solicitor' No. 1. You have up to 3 years to make a claim. Ask around for recommendations for another solicitor.