You need a (probably deliberately misnamed) tv licence if you watch any programme, from any broadcaster (not just the BBC) 'live' - that is as it is being broadcast.
You also need a licence if you watch BBC iPlayer, as of 2016 (September?) after the BBC had an amendment made to the relevant law.
You DO NOT need a licence, however many televisions or other receiving devices (tablets, PCs, phones, etc.) you possess or have on your premises and whether or not they are connected to anything, have aerials, etc., just because you have such equipment.
You DO NOT need a licence to watch 'catch-up TV' other than on BBC iPlayer; you can watch ITV Player, 4OD/All 4, Netflix, Amazon Prime Video, YouTube, Vimeo, your own DVDs, etc. to your heart's content on your television or other device without paying for a licence.
The BBC employs a third party company, currently Capita PLC, to check whether or not apparently unlicensed premises have residents who are watching 'live' broadcasts. These people have no more rights of interrogation, entry, arrest or suchlike than any other regular citizen.
You can withdraw access rights from Capita or anyone else - however anecdotal evidence from around the Internet and from people generally would seem to indicate that Capita view people who exercise WOIRA (withdrawal of implied rights of access) from their property with suspicion - which means they may snoop on you more assiduously. Personally I don't think doing this is worth it - the security checks Capita runs on its employees don't seem to be particularly good and some of its employees have been convicted of offences against the person (including rape). You don't want these people hanging around your home.
Capita employees work under the name of 'TV Licensing', but that is only a trading name owned by the BBC. This is not a official body.
Registering with 'TV Licensing' to state that you don't need a licence is a very hit and miss procedure. For some few people it will actually mean that you won't be contacted again for a couple of years; for most it won't mean anything at all. Either the record-keeping is at fault, or Capita employees in most cases deliberately ignore the information.
The reason Capita employees who work checking up on TV licensing at premises are so assiduous is that they are paid on commission. For every licence fee paid after a visit, they receive money; if they fail to meet certain targets, they are out of a job. Hence the bully boy tactics often employed (including telling lies, and this is well documented around the Internet and I personally have experience of this - twice) by Capita employees.
No evidence from detector vans has ever been used in court to secure a prosecution for watching live broadcasts without a licence. The BBC were finally forced to admit this under an FOI request in 2011 (tv-licensing.blogspot.co.uk/2011/04/bbc-confirm-detector-vans-never-used-in.html), and that situation still hadn't changed in 2015 (I can't find any later evidence yet published).
Despite everything TV Licensing/Capita/the BBC tries to imply, you do not have to produce evidence that you do not watch live broadcasts. As many people have said, one of the fundamental tenets of English Law is that a person is innocent until proven guilty.
The best recourse for dealing with this matter is to ignore TV Licensing completely. It might be fun to bandy words with them at the door, but these people often lie and some of them have been physically violent (for example Gary Catterick); many are verbally abusive.
So, you simply don't need to do anything. Don't answer letters, don't answer the door, don't speak to them, don't engage.
And you certainly don't need to 'detune' your television!
If anyone needs corroboration for any of this, I will happily provide links. I'm horrified by Neverender's misinformation and by some people saying they're paying for a licence they don't need just to stop being hassled. The Mafia work like this too - it's called 'protection'...