I would say the acoustics and layout at Mildred's make it one of the noisiest places in London to eat when it is busy. Tibits manages to be large and busy without being so intrusively noisy, although of course it is veggie not totally vegan.
I highly recommend Manna (Chalk Farm tube) which is also 100% vegan. I tend to get the mezze where you pick three starters as your main as the starters are the star for me here. The ravioli is fantastic and can be a starter or a main. Last time I was there they had a light, airy and delicious blood orange cheesecake.
On a separate note I was shocked to see inSpiral cakes are now £3.99 a slice at Wholefoods. For a while it was cheaper to buy their cakes at Wholefoods but now it is cheaper to buy from inSpiral.
Cat and The Cream cupcakes (available at Wholefoods) are now all both vegan and gluten free. Unfortunately this seems to have affected the texture and they are now harder and more dense than the vegan ones used to be. Also the Camden branch are stocking two flavours I haven't seen at Soho branch.