If an organisation owns website but another owns the name at Companies House, who legally has the name rights?

[Nick]

If an organisation name, lets say 'Fred Bloggs Holdings Colne Ltd' is registered at Companies House, does that registered owner have the legal right to prevent another organisation operating using that name as a website eg. http://www.facebook.com/fredbloggsholdingscolneltd?

In this instance, the website and FB page have already been running for at least 2 years and the organisation is not yet registered with Companies House. Would the existing website/FB page owner be given priority or the owner of the Ltd name at Companies House?

Furthermore, if it is in favour of the Companies House owner does that company then have the right to petition for ownership of the website and FB page?

[Apollenaire]

Whoever actually registered the domain name owns it. God could have been using he domain name God.com since he beginning of time and would not have legal rights if somebody else registered it yesterday.

[Who]

3 questions

1) No - the website can do whatever it wants, but it cant carry on any business as "fred bloggs. holdings......"

2) no - its first come first served at companies house

3)No - you must distinguish - a company registered at companies house can carry on business under that name. A website name is just a website name
The one has nothng to do with the other.
A company only has the sole right to trade under that name - it does not have a right to anything else. Companies house has NO say in what happens on the internet.