I put my booking deposit down on a second hand property two weeks ago and my solicitor contacted me today to say he received the contracts this morning, I should be able to sign on friday once i have the balance of deposit (arrrrggghhhh)! Legally i think you have 21 days from the time your sol receives the contracts but in your case you obviously want to move this along.... I dont know what happens after you sign the contracts or how long it takes before you have the keys but my estate agent reckons i should be in the house in 2/3 weeks. Really i think its a matter of pester pester pester...emails and calls to light a fire under their bottoms!
Best of luck with it all, its a very stressful but exciting time...