I think the best tip I can give is to do your research. Knowing what’s vegan before you go shopping makes it so much easier especially if vegan shopping is new to you.
Accidentally vegan foods are foods that are vegan without trying to be. There are things like peanut butter and houmous, and more surprising things like Co-op’s jam and custard doughnuts, or McVitie’s Hobnobs. Veganuary have compiled a pretty decent list here.
If it’s booze you’re looking for, Barnivore have got you covered.
There are facebook groups dedicated to vegan supermarket finds, they’re really helpful and definitely worth joining. If there’s anything you’re unsure about (E numbers, etc.) you can always post here and people will happily help you out.
Not everything that’s vegan is listed as vegan so you’ll have to do some ingredient scanning. Allergens are usually listed in bold or uppercase to help them stand out- this is great for spotting dairy products and egg. Look out for gelatine, tallow, honey and beeswax and check out Vegan Easy for a comprehensive list of additives.
If in doubt, Google.
Once you get used to it vegan shopping becomes second nature and you develop a sixth sense for sniffing out accidentally vegan products and bargains 🙂