Maybe as follows
Sub MoveRefNum()
Dim oItem As MailItem
Dim oDoc As Object
Dim oRng As Object
Dim i As Long
'Open Quick Turnaround email template
For i = 1 To ActiveExplorer.Selection.Count
Set oItem = ActiveExplorer.Selection(i)
Set oDoc = oItem.GetInspector.WordEditor
oItem.Display
Set oRng = oDoc.Range
With oRng.Find
Do While .Execute("Cust. Ref: ")
oRng.collapse 0 'omit this line if you need to add the Cust. Ref text to the subject as well as the number.
oRng.moveendwhile "0123456789"
oItem.Subject = oRng.Text & Chr(32) & oItem.Subject
Exit Do
Loop
End With
oItem.Close olSave
Next i
lbl_Exit:
Set oItem = Nothing
Set oDoc = Nothing
Set oRng = Nothing
Exit Sub
End Sub