Looking through here...
http://www.vfs-uk-ae.com/additionalservice.html
Especially, in your case...
You should be aware that you may experience extended processing times if any of the following factors apply, if you have:
overstayed a period of leave in the UK, and/or;
been refused leave to remain in the UK by the Home Office,
To make an appointment to use the premium service please email, telephone or simply attend the visa application centre reception in Dubai or Abu Dhabi and ask for the 'premium service'. Please see the 'Contact Us' page for details.