I had the same, from when DS3 was 8 weeks old, I had to be on a restricted diet while bf.
Now for some toddler snack suggestions. Bear in mind that my list might be more restrictive than you need due to DS3 being nut allergic too. And quite a few aren't GF, as he is fine with gluten.
So far, I have found : Tesco GF scotch pancakes are dairy, soy, nut free. (And GF/wheat free).
Baby Organix crisps, the pink prawn flavour stars, and the orange carrot flavour sticks are both dairy & soy free, but DS3 can't have them now as they started using nuts on the machinery around 3 months or so ago. Ditto the rest of the Baby Organix range.
The mini gingerbread men are dairy & soy free, as are the vanilla and raspberry puffs, and all of their rice cakes EXCEPT the cheese ones. All baby Organix range.
Tesco Potato cakes, Sainsbury's too. ASDA ONES HAVE SOY LECITHIN IN.
Orgran kids mini outback animals chocolate cookies are nut, soy, gluten, wheat, dairy, egg, yeast free and vegan. Really nice though!
The fruit factory fruit strings / fruit hearts / fruit stars are found near the raisins and/or down the baking aisle in most supermarkets, and are dairy, soy, nut free. They are dusted in maize starch.
And there's Zero Zebra rice milk chocolate sold by Allergy Essex (online shop). They do a plain version, a rice crispy version, and my personal favourite, one with freeze dried raspberry bits in. I really can't tell the difference between it and ordinary chocolate, except, if anything, it is slightly creamier! They are free from all of the 14 main allergens.
Lots of the value ranges of biscuits are dairy & soy free - Tesco value bourbon creams are dairy, soy, nut free. Often because they are cheaper because they replace the butter with vegetable oil. The value digestives are dairy, soy, nut free too.
With biscuits, look at value brands first, as they are far more likely to be safe!
If anyone else has any snack suggestions, I'm always on the lookout.
Oh - Coleman's seafood sauce is dairy, soy, nut free. DS3 loves having avocado and prawns for lunch with seafood sauce, or having cucumber and carrot sticks to dip in it.
Uncle Ben's Lemon and ginger stir fry sauce (in a jar, with an orange lid) IS dairy & soy free. So now I can even cook DS3 a soy-free stir fry!!
Heinz ketchup, steak sauce and barbecue sauce are all dairy, soy, nut free.
I slow cook beef brisket in a sauce made up of a bottle of Heinz barbecue sauce, a tin of chopped tomatoes, and two Oxo cubes.
• Oxo cubes are NOT GF or wheat free.
Gravy - I use either Knorr gravy pots, or Coleman's instant chicken/beef gravy (comes in a tube) for a dairy & soy free gravy. THESE ARE NOT GF.
Pre cooked mini sausages (with the picnic food) seem to be dairy, soy, nut free in every supermarket.
At least in Tesco (how can you tell it's my closest shop?!), there are lots of the other picnic snacks that are dairy & soy free. The mini scotch eggs. The chicken nuggets. The pork pies. MOST AREN'T GF.
Bird's eye chicken dippers are NOT dairy & Soy free...but Tesco own brand ARE.
Tesco bags of 30 cod fish fingers are dairy & soy free. Young's calamari are too.
Party food - lots of the Indian selections are dairy & soy free. Don't even bother with any of the Chinese ones. Sausage rolls - Tesco value use veg oil instead of butter, and are dairy & soy free.
Hope some of this is helpful. I will put some more things on here as I think of them.
As you can tell, shopping takes up a lot of my time...