Ah, this is like my household on a daily basis. I am a pescetarian (eat fish, but not meat), ds1 is allergic to eggs, beans, pulses and nuts, ds2 is allergic to dairy, pulses and nuts.
Oatly milk is a great substitute for cows milk for cooking and oatly cream is great as a substitute for single cream and is not sweetened like many soya creams. I use oatly cream to make mushroom strogonoff for example. Oatly milk and oatly cream are available from tesco and ocado.
I use coconut milk to make vegetable korma.
Tofutti soya cream cheese (from health food stores) is quite good - you don't get the nasty soya aftertaste you get with some non-dairy cream cheese. This does quite a good pasta with veg, tuna and soya cream cheese for something quick and easy.
Potato and leek pie (using oat milk to make the white sauce) with veg is also nice and easy.
Cheeseless cheesecake is easy using tofutti soya cream cheese too if you want ideas for sweet stuff.
Watch some of the quorn products as many have milk in though!
Of course, if you don't want to cook, the easy option with those restrictions is fish and chips 
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It's really not so difficult to adapt traditional recipes once you find good substitutes to use, but dairy can be difficult if you don't label check as it is everywhere!