It would normally be the solicitor who would receive the loan pack, not the broker, so once this is received by your solicitor, he/she will contact you to call to complete the contracts and all mortgage documentation.
Contracts together with a 10% deposit on signing of contract (less any booking deposit which you may have paid), will be sent by solicitor back to vendors solicitors with a completion date inserted (having discussed same with you), once the vendor is happy with completion date vendor will have to then complete contracts and one part will be returned to your solicitor. Only at this time will a binding contract be in place.
Your solicitor will also have to return documentation to your bank/building society and request monies for the completion date.
You must ensure that all insurances, assurances, valuations, direct debit mandates etc etc are in place for the bank, as they will not release any monies until they have all they request.
A period of two weeks is a little unrealistic, so I would say to you look at 3 weeks, provided everything is plain sailing for your legal team!