LDNmummy, I actually have been through exactly the same as you, I was dairy free from when DS was 12 weeks old as he was reacting to the proteins in my breast milk , he had his first skin prick tests at 6 months old as did my DD. I ended up bfing until they were over two as they wouldnt take the hypo formula. DS was a nightmare to wean as well, we couldn't get him to eat hardly any solids until he was about a year old, it was very frustrating. So I can empathise, and I didn't get from your post that the coconut yoghurt was for other reasons than just a pudding.
I used to buy dairy free probiotics for DS, which would be much cheaper than yoghurts at £5 a pop.
Dairy and soya free is hard, I was so delighted when DS outgrew the soya allergy.
I have to disagree though as I think it's easier for a baby to be dairy free from the start. DS has never had cheese, he's never had cow's milk or eggs, so he doesn't miss these things in the same way an adult going dairy free would after having eaten them, so I don't think you need to substitute in the same way.
It does take a bit of adjustment and a bit of research reading loads of packets to find what they can and can't eat, but it does become just normal eventually. We mostly eat dairy free as a family.
It's nice for them to be able to have ice cream etc, but I do think they just need to get used to the idea that very often they are not going to be able to eat things other people are having. My two are very stoical about it, they don't get upset that they can't have the ice cream everyone else is having and have an ice lolly instead. That's just the way life is going to be and they'll have to get used to it. Perhaps they will be less stoical as they get a bit older, I don't know.
I would also have thought that living in London, sourcing dairy free alternatives would be a lot easier than it is here in Scotland. When I was looking for rice yoghurts and ice cream for DS the postage was astronomical, whereas all the stockists listed were in London. Although it definitely has become loads easier and cheaper than it was 5 years ago to get alternatives,tesco now stocks dairy free cheese and Oatly and pure are quite often on offer.