Can the track even know what the speed of the train is, no.
Can the signalling system tell, maybe.
What can tell is a Network Rail employee or a contractor working for Network Rail, equipped with a radar speed gun. I've seen this happen.
Some Hot Axle Box Detectors (HABD) can record the speed of each train that passes over the site.
As said above, systems which take signalling system data can record how long a track circuit or axle counter section is occupied for. As the length of the section is known, the speed of the train can be calculated.
And computer based signalling interlocking records all signalling events including track circuit and axle counter data.
ERTMS will also record data.
Modern computer based axle counter systems may also record axle counter data.
The modern digital TI21/EBI track circuit equipment also records data.
There may also be separate monitoring equipment (provided for maintenance purposes) that records track circuit data.
For the most part, these signalling systems are not routinely used to check for train drivers overspeeding.
Of course, the TOC has access to the on board data recorder. If Network Rail has concerns, they can ask the TOC to provide a copy of this data.