What name you can call yourself

There is no U.K. law which specifically says what names you are or aren’t allowed to call yourself. However some names may be illegal, due to other laws.

Names which may be illegal

Any name which promotes racist or religious hatred is illegal.
Any name which promotes other criminal activities (e.g. murder) is also illegal.
Any name which could be blasphemous (e.g. “God”) may be illegal. Note that “Jesus” is used as a first name and is probably not illegal.
Any name which is also a trademark would not be illegal in itself. However, depending on your actions, you may end up infringing that trademark. E.g. if you called yourself “Coca Cola” and started selling soft drinks, you would infringe Coca Cola’s trademark.
You cannot change your name for any criminal purpose (e.g. fraud)—no matter what the name.

Names which are not illegal, but you may have difficulty using

Any name which contains punctuation (other than apostrophes and hyphens) is not illegal, but you will have difficulties getting people to enter your name in their computer systems. HM Passport Office will only allow apostrophes and hyphens on your passport, for example.
A first name such as “Lord” or “Sir”, which gives the impression that you have a title, is not illegal. However you cannot really change your title by deed poll—your “title” would not be officially or widely recognised, and you would actually be “Mr Lord Bloggs” (for example).
Any name which is vulgar or offensive may not be illegal (unless it promotes crime or racist / religious hatred), however it is unlikely to be widely accepted, e.g. on your passport.
There is no legal requirement to have two (or more) names, and some people do legally have one name only. However, you may find that your name is entered into computer systems as “X Bloggs” or “No Name Bloggs”, which may not be what you wanted.
Any name which is unpronouncable, extremely long, or difficult to spell is not illegal, but would just be inconvenient for you to use.

About changing your title

You can change your title (i.e. Mr, Mrs, Miss, Ms, etc.) at any time, and you don’t need a deed poll.

You cannot use a deed poll to change your title to “Lord” or any other such title. A title will only be officially recognised if you’re granted the title via official means (i.e. from the Queen, or whatever).