HMRC has guidelines about how long you have to work at a customer site before it is considered to be a fixed site like this. They have to do this because it informs tax decisions about travel expense claims.
I think the guideline is that after two years, the site should then not be eligible for travel expenses. Nearby sites are also not eligible - where the definition of nearby relates to how similar are the journeys taken to reach each site. Whilst HMRC clearly aren't the branch of government that are involved in this ruling, this is a similar structure around which such an argument could be made.
Even if it would apply to consultants though, I doubt anything would change. Right now there's already laws in place here (NL), or just a company agreement, about longer commutes, iirc any commute longer than an hour can be written down as working hours.
The issue is that you have no control over the location of these changing "fixed" offices, so your employer is free to assign you to a customer halfway across the country. Sounds exactly like the kind of situation this ruling is supposed to protect against.
IAN(Y/A)L