Upvote:5
Let's start by clearing up some confusion. ESTA is just permission to get on a plane to the US. The thing that admits you to the US is called the Visa Waiver Program (VWP). When googling what you are allowed to do, search for VWP, not ESTA. (To be fair, lots of people say ESTA when they mean VWP). Being British you are (very probably) eligible for VWP.
VWP gives you the same permissions that a B1/B2 gives you. Let's look at what you want to do:
Also a VWP is not going to give you more than 90 days in the US. For that you would have to apply for a B1/B2, but even then you would not be allowed to work.
By far the best way to do this is to have your meetings in the US under the VWP, plan the work, even hold design and requirement discussions, then return home and do the actual work in the UK. You can fly out reasonably frequently for more meetings. The only other way is to get some kind of work permit that allowed you to work in the US. I believe that work permits are obtainable if you can show that you have specialized expertise that is essential to the work and is not generally available.