Most of DDs friends at other schools seem to become free readers after lime. I think our school is unusual in having a reading scheme for most children right the way throughout.
Our schools says that they assess the books not just on content but also emotional maturity, so some of the Jacqueline Wilson books that are black are there not because they're difficult to read but because of the subject matter, and the school didn't want the children reading them too young.
So my DD is on blue, she's allowed to read some JW books, but not all because some are black.
However, there's no official scheme books like there is before lime, it's just the banding they have given each novel.
I'd say though that David Walliams, Roald Dahl are both suitable for younger readers along with some Michael Morpurgo. Those were the books my DDs enjoyed when little.
Enid Blyton is great too. Some of her stuff is great for little ones. For example Amelia Jane is a dead easy book, and my (good but not mensa style reader) easily read it in year 1. There's other less girlie ones too - but some of her stuff is really quite simple to read.
We do have a reading scheme which goes several levels above lime, Pearson's Bugclub, which is great and DS1 reads the non-fiction component of. The content is not suitable for him of the non-fiction ones, alas.
I found THIS really useful when I had an early reader. You can search for books by "maturity level" (they call it interest level) and by reading complexity. To work out approximate reading level, search for a few books you already know are appropriate and work out an approximate ATOS or Lexile range. It's only a guide and occasionally is a bit random, but I found it useful for avoiding distressing content/adult themes. I could then reserve library books online and swoop in and collect them.
I would imagine it would also be useful if you had the opposite situation (eg older reader who struggled but didn't want baby-ish books).
Oxford Reading Tree and Collins Big Cat go up to level 17 (diamond). My dd school uses them for assessment and guided reading for all children until end of year 3. IMO the books at the higher levels have more varied vocab and more complicated sentence structure than books like Whimpy kids or Secret Seven, that kids would read in their spare time at this stage. The series includes non fiction, more Biff and Chips (this time as time travellers) and abridged or in some cases retold classics like Treasure Island, Wuthering Hights, and Shakespeare classics. Our school has literally hundreds of different books between.lime (level 11,) and diamond (level 17).