You cannot use a word that is offensive or use of which would constitute a criminal offence. You cannot use 'Limited' or 'plc' (or their Welsh equivalents, or abbreviations of them), if you are not a limited company. You cannot use a name that would give "so misleading an indication of your activities" that it would mislead the public.
There are words that you cannot use unless you can justify them. They include British, International, English, Association and Group. There are other words that you cannot use unless you have written permission from a specified body. For example, you cannot use Royal, King, Queen or Prince unless you have a letter from the Department of Constitutional Affairs. You can't use offensive words, or words that imply a connection with central or local government or a public body unless you get permission from the DTI. Use of some words, such as 'Solicitor' or 'Patent Agent', is a criminal offence if you do not have the relevant permission. Lists of such words, and the bodies whose permission is needed in each case, is at www.companieshouse.gov.uk.
Take advice before using a name that is identical or similar to an existing name (see question six).