Having worked designing, installing and maintaining these systems both here in the UK and abroad, I can confirm that the issue tends to be cost.
In most areas, the bandwidth provided by the various cellular providers is ample; especially when balanced across multiple providers, and with the improvement in reception that a roof mounted antenna and other hardware provides. In some areas there will always be poorer signal, but the number of true "not-spots" on the UK rail network isn't as great as it once was.
The UK loading guage doesn't impact the installation of antennas at all - the size of the antennas is so small that it has no bearing on the trains kinematic envelope at all.
The issue comes from the fact that cellular networks charge a large amount of money for data still, especially on business contracts, and when you consider the amount of data that providing WiFi to a train load of people consumes it gets expensive VERY fast (unlimited data contracts rarely exist for this sort of application). You then have to consider the equipment that is used, as on-train routers, access points and switches are often more expensive due to the certification process they must go through. This hardware all then needs to be wired up and installed, which also costs money. There is also a substantial "on-shore" infrastructure required too, even if you don't use track-side networks.
Ultimately when most franchises/concessions now state that operators can't charge for WiFi, it becomes a very substantial cost centre that is second to actually providing a service that goes from A to B.
Various companies (including the one I worked for) have in the past used WiMAX and looked at other line-side radio technologies to provide backbone capacity, and conversations from a technical perspective have been quite advanced - but the point at which it stalls time and time again is working out who is going to pay for it, or when said organisation sees the price tag.
With the way the railway is managed in the UK, I wouldn't expect this situation to improve any time soon. Money is limited and train WiFi is quite far down the list of priorities.