Cannot enable Database Mail XP

I'm trying to turn on Database Mail.

I set the flag in db_config, did the reconfigure, and for good measure stop/started SQL Service (and thereby SQL Agent service too) [and I have since rebooted the server]. I have created a Profile (which I think is correctly set up)

If I try to send a test email I get

"SQL Server blocked access to procedure 'dbo.sp_send_dbmail' of component 'Database Mail XPs' because this component is turned off as part of the security configuration for this server. A system administrator can enable the use of 'Database Mail XPs' by using sp_configure. For more information about enabling 'Database Mail XPs', see "Surface Area Configuration" in SQL Server Books Online"

EXEC sp_configure 'Database Mail XPs'
GO

name              minimum     maximum     config_value run_value   
----------------- ----------- ----------- ------------ ----------- 
Database Mail XPs 0           1           1            1

so it appears that the setting is indeed set.

SELECT is_broker_enabled FROM sys.databases WHERE name = 'msdb'

gives 1

EXEC msdb.sys.sp_helprolemember 'DatabaseMailUserRole'

gives:

DbRole MemberName MemberSID
-------------------- --------------------------- -------------------------------
DatabaseMailUserRole Certificate_UseDBMail_Login 0x010600000000000901000000F6...
(my login is sysadmin, so should be OK unless I have done something goofy)

EXECUTE dbo.sysmail_help_status_sp

gives the same "'Database Mail XPs' ... component is turned off" error above.

I also, latterly, set "SQL Mail XPs", but that hasn't made any difference either

@@VERSION =
Microsoft SQL Server 2008 (SP2) - 10.0.4067.0 (X64)

EDIT:
Microsoft SQL Server Standard Edition (64-bit)
O/S = Microsoft Windows NT 6.1 (7601)
Is clustered = False

(Not the latest SP, I'm arranging for that to be installed in case that brings a solution, but that needs scheduled downtime which will be a while obtaining)

Thanks