No, they are advertiser funded - although C4 might get a cut of the licence fee in the next licence fee negotiation.
But they are already Public Service Broadcasters (PSBs) so as part of their linear (non digital) license they are held to certain standards including making news and domestic programming.
Channel 4 was specifically set up to be non-profit making, so the money it makes goes back into making programmes as part of its license. Had it been privatised last year as the government planned, it would likely have been sold to Discovery/Warner which would have put a stop to much of its UK based production, as it’s more profitable to buy in a lot of shows.
ITV and C5 are profit making, so they are less likely to get a cut of it. That means they don’t have to produce the same amount of PSB content, but under the terms of their licences they still have to produce news and UK based content.
Obviously the license fee system will change, and it may well be divvied up between PSBs in future.
But if it were to disappear completely then the PSB system would go with it, which would mean very little news gathering, and much much less Uk based content. If the PSBs become part of international conglomerates like Warner, they are solely profit driven as it will be cheaper to import content, and to make sure everything made in the UK also appeals to an international audience.
You also have to remember that streamers like Netflix and Amazon prime are running at a massive loss right now in the grab for subscribers so the higher quality content they make (clearly some of it is great) isn’t likely to be the main offering going forward. Same is true for the other streamers - none of them are making money and most of them won’t last.
So maintaining a Public Service broadcasting system is basically the guarantee against virtually all TV being shit, and some of it being bespoke made for UK audience.