The best stroll in London on a Sunday is through the famous Columbia Road flower market. This market takes place every Sunday from 8 am to 2 pm and is very touristy. As a result, I advise you either to go there very early to avoid the crowd, or to go towards the end where some merchants sell their plants. When I went, I did not follow this advice and there were a lot of people, making it difficult to move and to look at the plants.
Roses, tulips, succulents, daffodils, orchids, fronds and buttercups follow each other. Bright colours blend with perfumes, as you try to sneak from one stand to another to not miss anything. Finally, I took advantage of this excursion to buy 2 small cacti, 1 aloe, 1 bigger cactus and 1 big plant, all for about £10! Sometimes, a plant is cheaper than the flowers. A small rosebush costs £5, versus £5-10 for a bouquet of roses.
By doing this walk, I have actually been able to discover small super friendly shops nearby. In the ones I saw, there were quite a few nice decorative shops and of accessories for kids, but I did not have time to really explore because there were so many people. It's maybe better to visit them on another weekday.