The article The Windows 10 spring update no longer lets you disable web search in Start – workaround reports that the following registry update is required in Windows 10 version 1803 :
Windows Registry Editor Version 5.00
[HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Search]
"BingSearchEnabled"=dword:00000000"
AllowSearchToUseLocation"=dword:00000000"
CortanaConsent"=dword:00000000
You can just kill SearchUI.exe to have this kick in.
Source: windows 10 – How to disable internet search results in start menu post Creators Update? – Super User