Newbie2FT

Short answer: Yes, as UK citizens, you should be able to maintain your Global Entry membership even after you surrender your green cards, and, yes, placing your Global Entry membership number into the ESTA application will likely allow you to use the GE kiosk on your next visit. But there are a lot of considerations and middle steps you should think about.

Long answer:

Global Entry membership has been available to UK citizens since 2015. Once you abandon your US lawful permanent resident status and surrender your green cards, you will no longer be eligible for Global Entry as US LPRs but only as UK citizens.

Presumably, your and your wife's Global Entry membership would not be revoked after abandoning your LPR status and returning your green cards, as you would still be eligible for Global Entry, just through another category of eligibility. In other words, just by abandoning LPR status you would not necessarily trigger cancellation of your membership (suspension and removal from the program):

because you would still meet the program eligibility criteria:

In addition, while UK citizens initially applying for GE have a separate, additional UK Border Force vetting process, your change in status would presumably not require you to be vetted by UK authorities until you apply for renewal. (Note, though, that the procedures for UK citizen Global Entry renewal are seemingly not yet documented on the CBP website, because most of those memberships will not expire until 2020 or later.)

You should almost certainly make an appointment with the local Global Entry office on your final trip out of the United States or at the US Embassy in London, for several reasons:If I were in your shoes, I would make the appointment and discuss these changes with the CBP officer before completing an ESTA application and linking your Global Entry membership to your ESTA. That should hopefully minimize the hiccups from the change of what document your Global Entry is linked to (passport/green card → passport/ESTA). During the interview, you should probably tell the officer that you intend to apply for an ESTA soon and that you will link your Global Entry membership to it.

On a side note, are you absolutely certain that you wish to give up your LPR status?

If you are anywhere near 5 years in the US, you and your wife should strongly consider finishing out your green card terms and naturalizing before permanently returning to the UK.

The application to become a new green card holder has become much more complex this year, with significant increases in its complexity, ambiguity, and sheer number of questions. If you can afford to keep some type of home in both places, like a rented room in a house (†consult a competent lawyer for any details or planned actions or legal advice), you should really think about sticking it out -- especially if you need Global Entry because your work sends you to the US a lot.

There are no guarantees that the Visa Waiver Program will remain in place permanently and that travel to the US will always remain as worry-free as it is now for UK citizens.

Also, any children you have or adopt in the future may benefit significantly from US citizenship-by-descent (much broader job opportunities in the English-speaking world, in-state discounted tuition anywhere in the US under some circumstances, easier entry into some countries, easy NAFTA work permits for Canada and Mexico), even if they are not born in the US. Keep in mind that if Brexit sours UK relations with Europe in, say, 20 years, Americans may have an easier time living and working in Europe than Britons. (Downsides, of course, might include mandatory annual tax filings.)

And finally, as you know, some people give up their life savings or even their lives trying to become US citizens. Personally, I would suggest some major thought as to how to make the dual homes happen, with your primary one (main residence) in the US.