Derailment at White City 10/3/17

By law they will have been informed about it, and based on the evidence available to them at the time they will have decided whether an initial investigation was required.

If an initial investigation was undertaken, a view will be taken based on that investigation about whether to conduct a full investigation or not based on whether it is likely that there are safety lessons that can be learned from the incident. If they do decide to pursue an investigation a press release will appear on their website, except for very high profile incidents (e.g. the Croydon tram crash) this will usually be between about 1 and 4 weeks after the incident. For example the collapse of the cutting wall in Liverpool happened on 28 February and the investigation was announced on 13 March. Trackworkers were struck by ballast near Chathill in Northumbria on 16 February and the investigation was announced on 2 March.

At any point, if new evidence comes to light, the incident turns out to be more serious than first thought, or the RAIB has concerns about the internal investigation they cna choose to commence their own investigation at this point. For example the incident at Baildon, West Yorkshire where trains ran over a washed out embankment occurred on 7 June 2016 but paragraph 42 of the report states "Although the RAIB was aware of the washout soon afterwards, it was not aware that passenger trains had passed over it until 24 June 2016. […] The RAIB was informed of the incident by another source [i.e. not Network Rail or the train operator] and, having made preliminary enquiries, decided to undertake its own investigation."

It is certainly the sort of incident that the RAIB will consider investigating, but whether they do or not will be based on information that is not (to my knowledge) presently in the public domain.