Well if you choose the priority application, UKBA will make a decision within 10 days of your application. You can use this form:
Main applicant
Dependant
You will have to fill up the priority request sheet and email it to them after 8:30 am, and if you are among the first 30 people on that day, you can send in your priority application. Otherwise try again the next day.
This page roughly tells you what to do.
A friend of mine used this service and got her application in about 2 weeks, after paying 275 pounds more (her employer paid the fee for some reason). But I just applied for my visa using the normal online application form and got mine in exactly 2 weeks (10 working days) as well. (Ha! Take that!)