Do not legally complete on this home without inspecting it.
It would depend what is stipulated in the Contract which you have signed at Exchange.
However, the Contract cannot be unreasonable and must comply with the Unfair Terms in Consumer Contracts
Regulations 1999. It is usually required that the house builder give you 14 days notice for Legal Completion. In reality he cannot do this without risk, unless he has a CML final inspection certificate from the warranty provider. These should not be issued unless the home is 100% completed but this is NOT always the case so be warned!
The Consumer Code for Home Builders states:
The Contract of Sale should clearly define the notice period within which Legal Completion will occur; for example:
"14 days from the serving of notice to complete".
Be aware that Crest Nicholson's financial year-end is 31 October and Crest will want to shoe-horn as many legal completions as they can before this date, whether the homes are 100% finished or not. Last year Crest lost a Star in the HBF survey for Customer Satisfaction Star Rating. The Company stated it was because of delayed and postponed completions so there is history! I would be minded to delay completion until November if you are in anyway not 100% satisfied.
There is a reason why you are not being allowed to see your new home before you legally complete.
I suspect that your home is not yet finished and will be a rush job, built to a poor standard and may not thoroughly snagged.
The "New Home Demonstration" is for the site management to show you how the heating works and where everything is (Stop cocks, fuse trip switches etc.)
It is not an opportunity for buyers to inspect or snag, but for the majority it is the first time they actually see their new home in its "finished" state!
Regarding Brickkickers snagging your home, you are in a far stronger position if your independent inspection is carried out before you legally complete - before Crest get your money!
But there is no requirement that I am aware of for the builder to grant access for this, which is why Martyn said what he did.
At least I hope you can visit your home before you move in. Why not just turn up at Sales this weekend? They should have a key.