On a scorching hot day, the Story Museum in Oxford is exactly the refreshment required.

Visiting after a long-anticipated redevelopment, I I joined the audience in the spacious courtyard, enjoying our greatly appreciated ice creams and cakes from the cafe, whilst being entertained by a storyteller.

It is impossible to not feel artistic and imaginative when sitting in such a lovely atmosphere, with walls decorated with blue sky and clouds. Indeed, we were all transported away from Oxford and into the clouds for the story telling, in which Peter Chand, the resident storyteller, made us feel a wide range of emotions in a short space of time, extending between pity for these fictitious characters and an overwhelming sense of joy at the happy ending. In fact, the story was so heartwarming that I didn’t even notice a smile sneak onto my face until I was beaming from ear to ear. Looking around the courtyard, it was clear that I wasn’t alone in this feeling.

Peter Chand is an immensely talented storyteller and I hope to hear another of his stories, as he effortlessly blends between being energetic and completely calm. He told the story without anything written down or aiding him, as though it were created especially for this particular audience, including and captivating us all constantly. He had all the signs of a great storyteller; being able to fully entertain adults, young people and a particularly talkative toddler who went silent and just listened, all totally emotionally invested in a short tale.

The stunning design of the museum deserves to be seen by any fan of the imagination, with delightful details all over. A seemingly unimportant detail which pleased me was the cartoon superheroes on the toilet doors - nothing is boring in the Story Museum! Everything about the atmosphere of the museum, the relaxing storyteller and the charming story itself was wholeheartedly welcoming.

The Story Museum encourages everyone to be enthusiastic about the world of stories, no matter their age or experience with books. From the beautiful and inviting Small Worlds section inspired by children’s stories, to the enchanting Whispering Woods of spoken stories, everything is excellently adapted to be even more comfortable and safe than previously and everyone is immersed in the land of imagination.

The Story Museum is committed to being child-friendly, and this is just as true for its Story Café as it is for its exhibitions (these are currently closed for a period of redevelopment, but the café and shop are still open). I went in for lunch during the week, and found the place full of parents with babies and youngsters, all noisily and happily enjoying the food, the table chalks, and the brightly-coloured decorations (including Winnie the Witch's birthday cake, a Golden Snitch dangling from the ceiling, and a rather incongruous giant radish).

The café's menu caters for all tastes and dietary requirements, with gluten-free, dairy-free and vegan options. In keeping with the museum's family-friendly ethos, there are baby milk heating facilities, and a 'Hungry Caterpillar plate' available for little ones who are more into grazing on breadsticks and strawberries than tucking into a sandwich. Being even hungrier than a caterpillar, I chose the butternut squash and chicken salad, and an enormous brownie to follow. Because of the busyness of the café, however, the waitress let me know that there might be a slight delay in getting the salad to me, so I found a free table and tucked into the brownie first.

And what an excellent brownie it was. With a crisp crust and a squidgy middle, it was baked to perfection. The chocolate flavour was strong and sweet, without being sickly, and it went very well with the black coffee I ordered. I do wish I'd saved it until after the salad (which arrived quicker than I'd expected), as going from cake to vegetables was a rather odd transition, but I'll just have to be less impatient next time.

The salad was worth the small wait - the roasted butternut squash was full of flavour, and the balsamic vinegar, pesto and pine nuts added oomph to the dish. The chicken was well-cooked and tender - I did find a small bone and bit of gristle in one of the pieces, but that's an occupational hazard of eating chicken when it's not in nugget form, and didn't spoil my enjoyment of the meal overall.

The Story Café is a fun and eclectic setting - not the best place for a quiet lunch, perhaps, but an excellent venue for a family outing, a brainstorming session, or a lively discussion with friends. The menu has something for everyone, whether you want to stick to the salads or try something more decadent, like a Wonderland Sundae (definitely something I'll have to sample in the future). I left feeling full and satisfied - although still a little confused about that radish.

Brian Wildsmith was a children's book illustrator, whose brightly coloured works are instantly recognisable and much loved. His bright scenes, acute observation and rich detail must have burst into postwar Britain and injected real excitement and beauty. He died in September 2016, and his work is celebrated in a new exhibition in The Story Museum, showcasing original illustrations by Wildsmith, and by some of the next generation of illustrators who were influenced by him.

For many illustrators, showing just the pictures of a story might not make much sense. But Wildsmith went in for rich pictures which often show tension, or such a lot of detail that they seem to contain a whole narrative. He is probably best known for his illustrations of animals, and there are plenty of pictures here paying tribute to this theme. His animals are distinctive, realistic, and really animalistic, with no disneyfication. "Cat!" yelled my son (aged 2) across the room. It was a lion, and he'd picked out the wild feline stare.

The other main strand of Wildsmith's work was religious stories, and some illustrations from The Easter Story are a perfect example. The backgrounds are sparer with more white space so that the figures stand out. Wildsmith depicted people as beautifully as animals.

Around the corner are some works by other illustrators, with descriptions of how Wildsmith influenced them. Of course, there's a lot of colour, and a lot of animals, but it is interesting to see the difference in this group. There are old friends like Anthony Browne, and David McKee's iconic Elmer. But for me the most direct descendant of Wildsmith's style was Jo Empson, whose book Rabbityness was Wildsmithian in both realness of rabbit and explosion of colour.

This is a relatively small exhibition: big for The Story Museum in that it is all around the largest room, but small because with more than 80 books to his name any exhibition about Wildsmith could be quite enormous, and you feel for the rest of the alphabet, the jungle inhabitants and all the other artworks that aren't there. But it is perfect for children, and it feels like a grown up exhibition. A good introduction to galleries and art, and of course there is an opportunity to respond, adding your own artwork to a patchwork wall.

All in all a rich new addition to the Story Museum's existing works, and a good way to brighten up a grey day.