Chandrika, you usually have to unlock a domain before changing registrant data and or nameservers, and the switch is usually in your domain manager. The Lock/Unlock feature prevents unauthorized transfers and changes. Your domains are locked and changes you make to nameservers won't stick.

WHOIS for hairstylezone.com shows:
Domain status: clientTransferProhibited
clientUpdateProhibited

From their knowledge base:

"If you wish to use your domain name with another host there is no need to transfer your domain name to them. You may simply update the nameserver settings which they have supplied to you, to your domain name, via your domain control panel with UK-Cheapest. Nameserver changes can be performed as often as you wish for no charge. If you do decide to transfer your domain name away, then there is a one-off charge of £10 + VAT. This can be actioned also within your domain area, by selecting the Unlock option."

I have a hunch that you will find the Unlock option available in your domain control panel. Updating is fast now. Keep running WHOIS until you see the changes, then go back into your control panel and lock your domains.

-aerialx