The two bays are adjacent to each other, and the boundary between them is correctly marked, (the double-dashed line perpendicular to the kerb). In addition, the signs seem clear enough. So it's a bit of a puzzle as to why you didn't see them. Did you actually go and look at the signs at all ?
As against the above, the two signs are not ideally placed, because guidance on cases like this where two adjacent bays have totally different restrictions, is that the signs for each bay are placed on a single pole at the boundary of the bays, and arrows used on each sign to indicate applicability. However, the council are very unlikely to give way, so you would have to take them to London Tribunals and risk the full PCN penalty. If you're OK with that, then use the poor signage argument I have provided above.
There may also be a 'technical' appeal based on council mismanagement of the enforcement process which can win irrespective of the contravention itself. So wait a bit to see what might be suggested.
Is the vehicle yours, and is the name and address on the V5 up-to-date ?