If the workshop is training for the use of products sold by the UK employer to the US businesses, then this should be allowable activities under a B-1 visa or the VWP (though even in this can official language remains quite cautious).
If that is not the case, while some will probably argue that this is a grey area or even say exactly the opposite, my impression is that no, you are not allowed to do this on a B-1 visa or under the VWP: you are actually working in the US, and even though the funds transit through a UK business, you are effectively paid by US businesses specifically for the service provided.
When you see all the conditions for a paid speaker to be admitted under B-1 (must be invited and paid by a higher education institution, there is a limit on duration — 9 days — and on the number of engagements per 6 months…), you understand that no, you can’t just waltz in, provide a service and be paid for it, under B-1 status (otherwise it would just be too easy to just setup a foreign company to bypass all those rules). Check all the rules for the other cases listed, you’ll see that whenever there is a payment involved, there must be a significant part done abroad, not just billing…
Whatever you do in the US under B-1 status should be business, not work. Basically, it should be accessory to the main activity of the company, which must remain abroad. A common example is that a tailor coming to the US to take measures for a suit which will then be manufactured abroad (by the same company which employs the tailor) is fine, because this is business, the activity in the US is just accessory to the main activity.
But what you are doing here is a service by itself (again, unless it’s training related to a product already sold by the company which employs you, conditionally), and it’s not a permitted activity.
I’m at a loss as to the correct type of visa for this, though. I’m not sure there is one.