Hi Saudi,
This was what nearly tripped us up. The solicitor won't let you sign until you have the cheque and the bank won't issue the cheque until you have mortgage protection in place.
However, it sounds like you're only talking about signing the contracts. This shouldn't be a problem - you are able to sign these without mortgage prot.
Just to say though, start organising mortgage protection NOW. It takes longer than you think to organise and can cause more stress than it warrants. However, it is only valid for 3 months, so double-check the closing date within the next month or two in case there are delays with the new build.