If you do grow comfrey or nettles, when you cut it down you can tie it into an old pillowcase and hang it inside your water butt. This makes your water butt into a good source of plant food, essentially a comfrey or nettle tea. I don't really use fertilisers at all, I use the "no dig" approach, companion planting and crop rotation, adding homemade compost to raised beds in winter for the worms to incorporate into the soil.
Comfrey scavenges all sorts of minerals from deep down, so not only N, also deep rooting green manures will work on the subsoil & do the same. Compost of course also has a broad spectrum of nutrients - if you add urine to it as an activator that's full of all sorts of good stuff too
The stinging nettle infusion is good although it stinks to high heaven. You can also grow a patch of comfrey which doesn't sting but can be used in the same way. Or if it's an allotment grow a rotation of alfalfa (lucerne) then dig it under. I think all those are only for N though, eventually you will need some P and K - not sure where you get that other than blood,fish and bone meal or a mineral fertiliser?
An alternative to Growing Green (and aimed more at home gardeners, GG is really for commercial scale growers, though all the advice is easily scale-able) is Joy Larkcom's book Grow Your Own Vegetables. Its not vegan (though it is all organic) but there's plenty of advice on non-animal derived ways of feeding your soil. Its the best all round book on veg growing that I know.
Aaargh - wrote a long post which all got deleted! Will try & remember what I wrote . .
first thing - if you're new to veg growing, this book Growing Green will tell you all you ever need to know about vegan-organic growing.
Secondly, you really want to be thinking about feeding the soil more generally rather than fertilising the plants, if that makes sense. So, make as much compost as possible from weeds, kitchen scraps etc, think about growing green manures (sometimes called cover crops) over winter - legumes like field beans & tares fix nitrogen from the air so free plant food when you dig them in. Also (depending on whether you have a slug problem - its not always the best thing to do for all plants) consider mulching with any organic material you can get hold of, so grass cuttings, old straw, seaweed if you're near the sea etc etc.
If you do feel that specific plants need a boost (and you will need to feed anything grown in containers, grow bags etc) then there are plenty of vegan alternatives. Dilute urine is very good (and doesn't smell at all), though you have to be careful as you can end up with soft sappy growth from too much nitrogen if you overdo it. Comfrey or nettle 'tea' is excellent - worth starting a comfrey bed if you have space.
If you want to buy in a plant food then seaweed feed is very good for an all round tonic for plants that are looking a bit sickly, can't remember the brand name but at least one is Soil assoc certified.
Ash has its uses but be cautious as it is very easy to overdo it and tie up the nutrients in your soil. Its best sprinkled in thin layers in your compost heap.
Hope that helps - I would say that lots of non-vegan gardeners don't use any animal products at all other than maybe the odd bit of horse muck, and plenty don't have access to any muck at all, so its not a 'strange' way to be gardening at all.
So I know that a lot of people use animal blood and so on to feed their soil, and have some idea why this is useful. But I'm a vegan of the meat-is-murder variety and OH is a vegetarian from the meat-is-icky camp so this isn't the ideal thing for our fledgling onion-and-parsnip patch.
I've had a few suggestions, including -Menstrual blood, can't really do this as OH thinks it is yucky and will be working from home a lot over the summer so I can't do it sneakily -Pee, see above -Dilute coffee grounds, I do this fairly often and like that my soil has this addiction in common with me -Various chemicals, haven't done this as I want to stay organic -Ash, which I may try if we barbecue anything. (I had this idea of doing firepit cooking in the patch after we've harvested the veg, but OH points out this will likely be during the snowiest time of year) -Stinging nettle infusion, might try this one if I get a chance to pick some nettles in the woods. We don't have any in the garden.
Any more suggestions? I'm a bit new to growing veg because I've never had the sort of living arrangement where I can dig up the garden before.