And there are no trains at all today morning.
The problem can be twofold in situations like this. Firstly, sometimes a service may not be able to run on line X (in this morning's case, all roads of the GWML at Hayes & Harlington) for a time for safety reasons. For example, if the complex electronic signalling systems have failed due to an electrical supply malfunction, it is not safe to run services conventionally, and alternative signalling methods may not be able to be used for various reasons (not least of which may be a lack of a possible strategy to do so). Now, this means that no trains are physically able to run down the track.
Even if there is some technical workaround, or if there are nearby sections of line which could
in theory host services, this of course leads to the second part of the problem: the shortage of resources. All TOC resources are finite - they simply cannot have piles of trains, huge numbers of crews and loads of platform staff available in order to provide an unusual, limited service pattern a few times a year. In addition, even if the appropriate resources exist, they have to be moved (and this may not be possible due to such things as line possessions, a lack of alternative transport, weather problems and so on).
In this exceptionally brief description, I haven't considered crew hours, train classes permitted - or not - over certain routes (try putting a HST on the Greenford Branch

), congestion, track layouts, passenger flows, information provision, control room decisions based on different information sources... you name it, it affects a disrupted service.
Therefore, it is quite possible that trains are unable to run, even if the line where you are looks "just fine" to the untrained eye.
Now, with regards to speed... within a few hours, days or some other measure, it is sometimes possible to ease the situation, and start running the service. If the resources can be put in place for a significant proportion of the downtime, alternatives can be operated. Speed is crucial, but sometimes it isn't worth it to try to provide alternatives or complicated emergency service patterns, as a more optimistic solution may be found shortly. In addition, preparation and complex strategic decisions are needed to move staff, stock and equipment.