This forum is about wrong numbers in science, politics and the media. It respects good science and good English.
I think the S4C (which I believe stands for "Channel 4 Wales", with the acronym being in Welsh) channel was a result of strong lobbying for such a channel by Welsh nationalists (preserving the welsh language has always been the centrepiece of Welsh nationalism) in the 1970s and capitulation to their demands by Willie Whitelaw.
I was a bit puzzled about you saying that S4C was connected with the BBC, but after checking the Wikipedia page on S4C it looks like the BBC took over the funding in 2013.
Previously it got most of its funding from the government, apparently from the Department for Culture, Media and Sport (DCMS), and it also received a small amount of advertiser funding. The government funding has now been offloaded on to the BBC, which of course means that the UK TV licence fee payer is picking up the bill.
Welsh language TV is an example of what I think public service broadcasting (PSB) genuinely is, non-commercially viable TV, but I don't think it's fair for UK TV licence payers to fund something as over the top as this. The Wikipedia article quotes a statistic from a leaked document that 196 out of 890 programmes transmitted over a three week period in 2010 had zero viewers. It would be more reasonable for the government to fund it directly (as it was doing), or for the TV licence fee payers of Wales to fund it.
The big problem for people trying to promote the Welsh language in the UK is that the UK's predominant language, English, has turned into the major international language thanks to the internet. English has achieved what 'Esperanto' was trying to do, and it's like the modern day equivalent of Latin. It might be better for Welsh nationalists if they gave up with the promotion of the Welsh language as their main cause and tried another approach. Scottish Nationalists have done pretty well for themselves without showing much interest in promoting Gaelic or whatever the native Scottish language is called.
In regard to Farage's proposal that the BBC licence fee should be reduced to a third of the current fee, I noticed this comment in a speech given a couple of weeks ago by James Harding, the BBC's current Director of News and Current Affairs:
The paragraph about Farage is this one:
"I’ve been asked whether politicians made the link between the BBC’s election coverage and the future funding of the BBC? Mostly, not. But, along the way, there were people from all parties who made the connection between their dissatisfaction with the election coverage and the fact that the next government will set the licence fee and the terms of the Royal Charter. Some did so explicitly. Nigel Farage, for example, said he was unhappy at UKIP’s treatment on the BBC and proposed cutting the licence fee by two thirds. Others left it hanging in the air."
Harding is conflating two separate issues there. Farage did complain about the treatment of UKIP in a TV leader debate hosted by the BBC, but he didn't mention this specific issue in connection with his proposed licence fee cut.
If the licence fee was cut back to reflect a more rigorous definition of public service broadcasting, it is actually unlikely that this would have much impact on the BBC's bias. Many right-leaning critics of the BBC regard Radio 4 as being the centre of gravity of the BBC's political bias, and Radio 4 would most likely survive a drastic cutback to PSB broadcasting as there isn't a commercial equivalent of Radio 4 as far as I'm aware. The BBC's bias comes mainly from its employees, and in principle there is no reason why the number of employees or their political views would change if the licence fee was heavily cut back and the BBC obtained the rest of its money from advertiser funding instead of the licence fee payer.
I suppose I should also comment on this paragraph in Harding's speech:
"But there’s criticism of the BBC’s newsrooms that is unfair and unfounded. Take, for example, the fabled left-wing bias. I find this increasingly hard to take seriously. In the light of the Conservative victory, what’s the argument? That the BBC’s subtle, sophisticated left-wing message was so very subtle, so very sophisticated that it simply passed the British people by? For some politicians have complained about this alleged bias, but not, in any meaningful numbers, the public. Or consider the criticism that BBC people are all in the grip of some public sector groupthink: how does that square with the fact that a Conservative Prime Minister, a Tory Chancellor, a proudly pro-enterprise Business Secretary and a London mayor who is a cheerleader for the City all recruited their spokesman from the serried ranks of pinkoes at the BBC. By the way, I find equally implausible the Labour critique that the BBC is too right-wing. Let me be clear: the BBC is scrupulously impartial. Of course, we make mistakes. I’m not saying we’re perfect; but we are impartial."
Harding is arguing, like Ian Hislop did on an episode of "Have I got news for you", that the BBC can't be left-wing because the Conservatives won the 2015 General Election. This argument would carry a lot more weight if the Conservatives had been winning general elections for the last twenty years. The last sentence also touches on the way that the BBC tries to do impartiality, it does it by being biased to the centre ground or 'metropolitan liberal' position. So it appears left wing to a grassroots conservative and probably right wing to some lefties. The proper way to do impartiality would be to reflect a range of political views (Channel 4 is a bit better at doing that).