If there is a company called, for example, The Wooly Jumper Company (London) Ltd can the name The Wooly Jumper Company Ltd be registered too as a different business?
-- Edited by matt123 on Monday 6th of January 2014 02:56:01 PM
Take care to differentiate the new company from the existing one. Otherwise, there's still a risk that you could be seen as trying to pass yourself off as the first company, especially as it could look like you would be following similar trades. Geographical location is often enough to show that difference, or if one is a knitter and the other a retailer, there is less scope for confusion.
Also, make sure that there are no registered trade marks that could be infringed. If Wooly Jumper Co (London) Ltd has registered "wooly jumper" as a trade mark, the new company could still find itself in trouble, notwithstanding that Companies House let the it register under that name.
(Mind you, if you register the trade mark, you could force the old company to change its name, or even cut its business out from under its feet!)