Nothing personal about a VRM, it's on show 24/7.
We need to see the council's photos. Also, the VRM would indicate (by virtue of the year number) whether the car might be leased or hired. But we can put this question now: are you the registered keeper with current DVLA registration or is the vehicle hired/leased? The latter introduces specific procedural considerations for us the assess.
You say you thought you were on SYL, so we need to see the condition of the lines and markings to form a view as to whether this is unsatisfactory and could be attributed to the council. We look at GSV over time to assess the degradation of lines and the council's approach to maintenance. Was the incursion merely trivial or as the result of misjudgement etc?
Your situation would get a thorough examination but we need objective photos to feature in the mix.
And this is before we look at possible mitigation