Try calling up early during the day or just before the end of day. This would be 9am UK time and 5pm UK time. Its the least busy time you probably could find and be persistent about it.
Another number you could try is 0114 2591894 as this was posted sometime back. I am trying to access the HO website so that I can reconfirm the phone numbers but their website is not loading. Perhaps you could try later. Click on
this weblinkto go to their homepage and following the links to the HSMP main page. You can also download the Urgent Treatment form, fill it up and fax the details along with the evidence, such as securing a job. You should then call up the HO to confirm that they have recieved the fax and have placed your application in the urgent treatment queue. It your urgent plea is accepted, I would expect a fairly quick turnaround of 2 weeks.