If you are booked to be despatched you wait. You don't suddenly decide that because it's time to go and nobody is there to despatch you that you can go, the Despatcher could be dealing with something else. If after a few minutes then a phone call to Control to ask why there's nobody there to despatch you, Comtrol may then authorise you to self-despatch.
That's not how LNWR operate. There are mandatory dispatch stations such as New St and Euston (and others), and there are self dispatch stations. Now if I'm at a station that is normally dispatched such as Runcorn and there are no staff then yes a call to control for authority would be the way to go.
According to the WMT route guide as produced by Ops Standards, Nuneaton is a self dispatch station. If there is a dispatcher on the platform, you use them to assist you. If there's no staff on the platform, you self dispatch as you do at all the other non-mandatory dispatch stations.
As an example, yesterday I arrived onto platform 5, the dispatcher was attending to the Avanti service on platform 4. Both trains had the signal and were due to depart. I self dispatched as he dispatched the Avanti, that happens quite often now.
Other TOCs clearly have different ways of working and I can only describe how if works on my TOC but that is how we do it.