The datum is defined by the original control survey.

Although a national mapping system may have been used in preliminary work such as route planning, the high accuracy control work for the project would normally be carried out using GNSS. This measures vectors in the WGS84 coordinate system, so what matters is the datum of the higher level control.

In the UK, for instance, it is probably the case that the starting point for the control was Ordnance Survey Active Stations, which are in the ETRS89 datum. So the coordinate system in use for Crossrail (for example) is XRail09, but more formally might be referred to as SnakeGrid XRail09 on the ETRS89 datum

Essentially, SnakeGrid can be used in association with any datum that uses the GRS80 ellipsoid or an equivalent – which really means any modern satellite-based datum such as ETRS89, NAD83, GDA94, etc.