A solid white line along the carriageway would usually be used to indicate either the edge of the road, or (if used in the centre of the road) to denote that the vehicles on that side of the road should not cross it unless it is safe to do so in order to turn right, or pass a stationary or slow moving vehicle or pedestrians.
As such, the usage of the solid white line painted next to the cycle lane would suggest that cyclists should not move out of the red painted area onto the main carriageway, although it would be perfectly legal to do so.
That being the case, if I were cycling along there, the fact that the raised kerb is painted solid white, would also suggest to me that staying in lane would be advisable. So one should really be cycling with care anyway and avoid crossing the white painted line, whether raised or not.
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