Let's put aside terms like 'fibre' and 'unlimited' and simply concentrate on actual download speeds (which is what really matters):
The minimum speed required for streaming services, such as iPlayer, Youtube, etc. is nominally 2 Mbps but I'd suggest that around 5 Mbps would be better to ensure a reliable service. So if you live on your own (and you don't get visits from hordes of teenage grandchildren, all demanding access to your wi-fi), a service providing, say, 8 MBps is perfectly adequate for catching up on Eastenders with iPlayer while simultaneously doing a bit of web browsing. My own broadband connection gives me about 10 Mbps and it's more than adequate for my needs. [Note: The only exception would be if you wanted to permanently download, rather than simply stream, really massive files such as movies; they'd take ages to download at such speeds].
If you live with someone else and you might possibly both want to stream different data-heavy services (such as Youtube and iPlayer) simultaneously, you could probably get by well enough with around 10 Mbps (or even less) but, say, 20 Mbps might be a better figure to aim for.
It's only households full of teenagers, who all want to stream Youtube videos simultaneously while Dad watches Eastenders and Mum does her Open University course online, who need higher speeds. Millions of people waste their money by paying for services offering 80 Mbps (and higher) when they'll never need anything like those speeds.