Waterfox Browser
I went looking for an alternative and tried all the main opposition to Firefox and none of them really offered what I wanted.
It was purely by chance that I stumbled across Waterfox - I'd never heard of it before, but now I use it as my main browser, with Firefox also installed for banking and shopping etc.
Here's the 'official' spiel:
Waterfox was started back in March 2011 by myself (Alex Kontos),
a 16 year old student. I had a fascination for the web and wanted to
help expand on the ideals of what Mozilla had for a free and open web.
And so I decided to make Waterfox, a 64-Bit browser based on Mozilla's
free and open source platform.
Waterfox was one of the first widely distributed 64-Bit browsers on
the web and quickly gained a loyal following. At a time Waterfox had one
thing in mind: speed, but now Waterfox also attempts to be an ethical,
user-oriented browser.
Waterfox focuses on giving users choice. The browser is focused on
power users, which lets you make the important decisions. There is no
plugin whitelist (meaning you can run Java Applets and Silverlight
apps), you can run whichever extensions you like (including Classic
Firefox Add-Ons!) and absolutely no data or telemetry is sent back to
Mozilla or the Waterfox project.
If you fit the profile I mentioned, I recommend giving it a try. It's certainly left me the most content I've been with a browser for several years.