Section 50(1) Local Government (Miscellaneous Provisions) Act 1976 wrote:
Provisions as to proprietors
...the proprietor of any hackney carriage or of any private hire vehicle licensed by a district council shall present such hackney carriage or private hire vehicle for inspection and testing by or on behalf of the council within such period and at such place within the area of the council as they may by notice reasonably require...
Not saying I necessarily agree, but would guess Wolves would argue that from the licensing authority's perspective the above is optional rather than mandatory. So there's no obligation on the council to test cars within its area.
What the above does mean is that if proprietors are called for a test within the council area then they must comply. The heading suggests that the section is addressed primarily at vehicle proprietors rather than the licensing authority.
By the same token, presumably the section means that if Wolves calls a car operating in Blackpool for a test in Blackpool then the proprietor could refuse to comply, because the section above only gives the council the power to call cars for test in Wolverhampton.
But if a Blackpool proprietor refuses to attend a test in Blackpool, then Wolverhampton Council could force it to attend a test in Wolverhampton by virtue of the section above.
But, in practical terms, which proprietor in Blackpool running a Wolves-plated car is going to object to attending a test in Blackpool if Wolves Council could then force it to attend for inspection in Wolverhampton?
So in practical terms, it suits all parties involved.
And even if it's arguable that what Wolves Council is doing doesn't comply with the Act, what in practical terms can any aggrieved party do about it? Apply for judicial review, I'd imagine would be the way to go about it, but who's going to do that? Other local authorities? Competitor firms who use locally-plated cars?
Again, in practical terms, it looks highly unlikely that anyone is likely to have the resources or justification to challenge it - judicial review isn't for the faint-hearted, and requires deep pockets.