As you'd expect,
good dentists in central London aren't cheap. It took me a long time to find a London dentist I could trust but wasn't extortionate (I lived in London for almost 20 years). And finally I found one!
I recommend Metrodental. They're at Liverpool St and Monument (so both practices are in the City). I've been using them for several years now and am so happy with them that now I've moved to Hong Kong, I still fly back to London to use Metrodental. And I'm aware of quite a few expats who do the same from all over the world.
http://www.metrodental.co.uk/
Their fees are listed on their website. It lists root canals from £325.
They're lovely people and at the top of their game. I definitely recommend you getting in touch with them.