What is a good vegan substitute for heavy cream

Thank you so much for all your guidance, really appreciate it!

Here's a link to an adapted version, as I don't have the actual book in front of me:

https://craftycooknook.wordpress.com/2014/05/23/cloudy-with-a-chance-of-godzilla-creamy-mushroom-almond-milk-soup/

Don't know if I'm too late with this, but Sarah Copeland's vegetarian cookbook "Feast" features a mushroom soup recipe that calls for almond milk instead of cream. Might want to give that a shot.

If coconut milk has too much coconut flavor, you could try using some cashews, macadamias, or walnuts that have been soaked in water for a few hours (overnight is best). Either puree with water to make a cream-like liquid, or add directly to the soup if pureeing the finished product. They will add a wonderful richness and creaminess to your soup!

Or "creaminess" by way of a potato (yukon or something similar preferably) or some cooked rice (if pureeing).

Thank you both! Will let you know how it turns out :)

Coconut milk will give a creaminess but I always taste it in the flavor profile of the soup. You could use cashew cream, which adds richness and has a more neutral flavor.

You can make the cashew cream by blending 2 parts water to one part cashews. If you don't have a Vitamix or other high speed blender you can get a creamier result by soaking the cashews for an hour or two before blending.

Coconut milk might have too much coconut flavor for a mushroom soup, but that is usually what I use as a substitute for heavy cream.
A combination of vegan sour cream and non-dairy milk mixed together until it's the right consistency could work and would taste delicious. If you want something less processed, then silken tofu thinned out with non-dairy milk might work too.