I'm nitpicking but I feel it's worth pointing out that not only do UK viewers of live TV need a license but all taxpayers contribute to the BBC by separate payments from direct taxation.
UK ISPs appear to throttle iPlayer traffic so ironically using a proxy might be worthwhile in the UK too.
The bbc is almost entirely funded by the licence fee. There is a small grant to cover world service (mainly for political reasons eg providing news in Arabic) and BBC worldwide makes some money, but the vast majority is from the tv license.
From you Wikipedia link BBC income includes "£279.4 million from government grants;". That's about 6% of the amount taken from license fees, I'd argue that's not insignificant. Financial information about treasury spend on the BBC seems quite hard to find however.
On point 2 why would the BBC be spending money to develop a system to indicate throttling if there wasn't even an "appearance" (as I claimed) that there was some throttling. Surely they'd want to show at least that there was an appearance of throttling before starting such a project?
FWIW my own experience with one of the top UK ISPs has been of quite poor service for iPlayer - significantly lower bandwidth is used for iPlayer connection than for other streaming sites. That is watching the same show in low quality on iPlayer I get significantly poorer connection than watching in higher quality streaming from some other site - this gives the appearance that iPlayer is being throttled.
UK ISPs appear to throttle iPlayer traffic so ironically using a proxy might be worthwhile in the UK too.