Do SMS messages also get delivered on WiFi?
No they don't.
3 years on and O2 are still trying to figure out how to do it.
You will need to call customer service to enable it on your account first.
Please call to check.
What it says in your MyO2 means nothing if it's not active on your account.
Track usage, upgrade and get support with the My O2 appDownload My O2