Not really any Walmarts in UK, they're linked to Asda stores but is a supermarket chain for foods and household items really, not aquatic stuff.
Have not been to an Asda for years so may have changed a bit now!
I use Maidenhead Aquatics for most of my plants, and fish stocking as well. But other items like test kits and aquatic equipments I find cheaper shopping online.
Some garden centres with an aquatics store (usually fairly small) has aquatic plants for sale as well.
Be warned however, if you see plants for sale at aquatic stores that are outside, in large planted water tanks types, these plants are likely to have pest snails at best or even worse damselfly nymphs or dragonfly larvae and/or eggs which believe me, you do not want the latter two in your tank.
I don't mind the snails at all but a lot of fishkeepers do not like them!
If you do buy plants form LFS and/or garden centre, make sure you do research BEFORE buying the plants to be sure they are aquatic plants. I bought 3 plants from LFS which were in water tanks in store and later found they were not aquatic plants at all, houseplants, these 3 plants are now in pots on my lounge windowsill and growing pretty well!
When you get plants, make sure you wash them thoroughly, I do mean thoroughly!
Tips I wish I learned before buying my plants for my first tank. I had 3 damselfly nymphs in my tank, all probably from the same plant as eggs, was a royal pain in proverbial to get rid of these!
This forum also sell plants as well in classifieds so, worth a look.
Good luck and do let us know how you get on or ask for any advice if you get stuck or unsure.