Multiple people are quoting the old approval letter containing the following - beware that this is outdated:
If you are a UK citizen and applied for Global Entry, and you are not a U.S. lawful permanent resident (green card holder) you must bring an original copy of your ACRO Disclosure Certificate (police certificate) to the interview.
This no longer applies: if you applied via the new UK home office system, you should have entered your Home Office approval code during the GE application in GOES. (In fact GOES shouldn't even let you apply without this code unless you're an LPR.)
All I had to show was my approval letter, passport, and permanent resident card with my residential address (for a different European country where I currently live).