That's a short timeframe, but I think the FAFSA is the most significant step, as most schools recommend that you start that sometime in February for the term beginning in the autumn. Once the SAR is complete, the process for Stafford loans was pretty straightforward, IMO. I would check with your program's Financial Aid Office for recommended timeframes, though.
Also, a quick update on my loan application process as well -- it doesn't look like JPMorganChase offers private loans for LBS anymore, so that doesn't leave much for the private option (CitiAssist, Discover, etc. are not available for London). On the plus side however, LBS is now certified for the federal GradPLUS loans. At 8.5% fixed, it's a better deal than my private loan quote, so I just called
Sallie Mae to cancel their private loan offer and start a GradPLUS loan disbursement instead.

It'll have to do for the first year, and then I'll see in '10 what the private loan environment looks like for the second year.