The kind of purposes that are allowed for a VWP visit are exactly the same as are allowed under a B-1/B-2 visa, so there are only two possibilites:
- Either using the VWP is fine,
- or the consultants need to get work visas, in practice a H-1B or L visa. These generally require that there's an US employer sponsoring the application.
Whether the work the consultants will be doing is a permitted "business-visitor" activity is not easy to say based on your description. Broadly speaking, the distinction is between whether what they do is in support of the foreign company's economic activity outside the US (such as sales, participating in meetings to coordinate joint activity, or helping install equipment bought from the foreign company, or train local personnel in its use), or it is separately productive work in the US (which earns money independently of anything that happens back in the UK). The latter is not allowed. But there are no crisp rules to tell you which side of the line you're on -- instead there's several decades of precedent from courts and administrative boards, which is not readily summarized.
In any case, if you're the employer and being denied entry would have serious economic consequences for your company (such as losing large customers or defaulting on a contract), you ought to spring for tailored advice by an actually qualified immigration lawyer, rather than what random people on the internet say.