I teach violin and piano. About half of my students do exams, the other half don't. For ensembles, like the youth orchestra, usually a recommendation from the teacher suffices. So if I said "yes, this student is playing at a grade 3 level" they would take my word for it. For more serious groups like the NCO, there is an audition process.
Just so that you know, if you/he would like to get validation for his performance level, without the stress of "proper" exams, you and the teacher can look into ABRSM Music Medals (accredited) or LCM performance assessments (non-accredited). Both are done by video submission.
Music Medals would be marked by his own teacher. They can be done during lesson time and the highest, platinum, level is roughly between grade 3 and 4. He'd need a duet partner for silver and above. I use these with my younger students and prefer them to exams in some ways, not least because they are less stressful. They have different requirements and you can choose between different musicianship options rather than having to do aural and sightreading. One of these may suit your son rather better.
LCM performance assessments don't have to be filmed in one go and they just involve the performance part of the exam, i.e. the three examination pieces (or three "sets" for traditional fiddle). You can film one piece at a time, then submit the three chunks of video on one DVD (I haven't used these but I'm pretty sure that's how it works).
In other words, there are ways and even nationally recognised certificates to prove that the level has been achieved without going through the formal examination route.
There are big technical leaps between grade 1 and grade 4, though the one that springs to mind is the use of third (and sometimes second) position as well as extensions in first position and more complicated keys that don't sit nicely under the hand. So far the best tutor series I've found is a new one by Robert Trory, entitled "violin playing". It's not "fun", there are no pictures, but boy is that series full of useful exercises as well as some lovely tunes. Book 2 covers grades 1-2 requirements including more complex finger positions, chromatics and simple double stopping; book 3 covers requirements for grades 3-4 including the position work and more complicated bowing styles. But your son's teacher probably has something that he/she uses already - I only mention this particular series because it's new.