Most lenders at the moment are being very selective on who they lend to and how much they lend.
Most high street lenders are currently capping their loan to values (difference between mortgage amount and value of property) at 80-85%.
There are however a few that will lend more than that, however as it constitutes a higher risk to the lender, the rates will be slightly higher than those of other lenders.
I recommend that you contact an independant mortgage broker who will be able to research the whole of the market for you, as you may struggle with the high street lenders.
As far as the time scales are concerned, I think that 3 weeks is pretty much near on impossible, and your friend may have to make soem alternative living arrangements for the time being.
Good luck