It's easy really. Are you ok with soya?
Alpro do a load of products these days: milk, yoghurt, desserts, etc. Soya milk works easily in cooking, including the cream.
All major coffee chains (and most small cafes even these days) sell drinks with soya instead of dairy. Swedish Glace ice cream is what you're looking for too.
If you can't do soya, then Oat or coconut are next alternatives. Oat makes me retch personally, and I can still taste the coconut, but it's true that it isn't a strong flavour
Pure is the best df margarine.
GF: Rice is your new friend. Stir fry, risotto, all sorts of rice stuff - even rice pudding. Potatoes are also good - so many choices for potatoes.
Pasta - any supermarket does their own version and there are some brand ones too - salute is good.
Bread - Genius is best imho - I like the seeded one best myself.
Breadsticks and crackers - look for DS brand
Biscuits - Nairns
Breakfast - porridge, granola, rice krispies
The best place to start your journey is prob Ocado's website. Even if they don't deliver in your area (and are a bit pricey) it will allow you to filter on DF and GF so you can see what's available.