At no point had the Pilot reported being IMC, requested an IFR Clearance, or was able to conduct an IFR Approach Procedure for his intended landing site.
Just to clarify that point. There is no IFR approach at London Heliport. It appears that there was no need for him to have asked for an IFR clearance in transit because the conditions did not require one, bearing in mind that the previous plan was to return to Redhill. The fatal mistake was to descend into fog lifting into low cloud. It may have been that the pilot misidentified another bridge along the Thames for Vauxhall bridge, easily done in marginal visibility.
For an experienced helicopter pilot, VFR is easy. IFR is also relatively easy. It's the bit in between that catches people out, as appears to have been the case here.