Overview
Currently, yes, a naturalised British Citizen can live anywhere in the world without losing UK citizenship - so long as they intended to live in the United Kingdom when they requested and were granted citizenship.
There's a strong precedent for this structure to remain intact, but the rules may of course change as the political situation changes.
The most useful reference documentation on this is the UKBA Precedent Based Scenarios document (see the PDF on that page, section 8: 'Deprivation' on page 25 (PDF Page 26)). Unfortunately the document is quite old, and doesn't take into account certain recent developments.
The Importance of Intent
It's important that a person seeking naturalisation intend to remain in the UK. They should have "thrown in their lot" with the UK, and be intending to live in the UK for the rest of their life. In short, the oath of loyalty is more than a formality, and British Citizenship shouldn't be considered a tool to be acquired.
In certain circumstances, people have claimed and been provisionally granted citizenship, only to have it revoked because they have left the country before they took the oath. For more examples of this, see the "Precedent Based Scenarios" document referred to above. Specifically relevant sections are "NATURALISATION S. 6(1): FUTURE INTENTIONS" on page 46 (PDF page 47), and "OATH OF ALLEGIANCE" on page 70 (PDF page 71).
Once legitimately gained, though, citizenship is not currently stripped when people leave the UK for any length of time. This includes leaving the UK permanently.
Scenarios where Citizenship is Lost
The technical term for this type of loss of citizenship is "deprivation of citizenship".
Deprivation of citizenship is taken very seriously, and occurs very seldom. Between 2002 and 2013, 37 people were deprived of their British Citizenship. Generally, this occurs only in a fairly limited set of scenarios. One of the key considerations is whether retention of citizenship is for "the public good", and this is decided on a case-by-case basis.
Examples of Loss
For further details, see the "Deprivation" section of the UKBA Precedent Based Scenarios document linked above.
- Espionage. There is a long history of spies for foreign governments being deprived of their British citizenship.
- Terrorism - this is currently the fastest-increasing reason for loss of citizenship (source)
- Serious criminal activity (often where British citizenship is being used as a tool to further the criminal activity), including:
- Cases of serious fraud and smuggling, where British citizenship is used to help further illegal operations.
- Certain cases of bigamous marriage have been considered for deprivation, though my understanding is that cases did not progress.
- Various other serious criminal convictions.