The Guardian puzzles are free online here:
https://www.theguardian.com/crosswords
(though that's presumably where you found the Everyman?)
They do one every Monday called the Quiptic, was is about equivalent to the Times Quick Cryptic, and is often a lot of fun (watch out if the compiler is Anto, though!)
An advantage of the Guardian puzzles is that the compiler is always named, so, with experience, you have some idea of what style and tricks to look out for.