...when do people feel it's appropriate? And what sort of vibrato would you use?

I'll pop my opinions on here once I've heard some of yours...

Jazz - fast and wide. Probably using jaw movement to generate.
Modern/romantic - happy to use a little gentle vib to add tone colour to longer notes.
Earlier - would avoid except maybe for a little on long notes to add warmth in a slow movement. Generated from diaphragm.

I see vibrato as a colouring to be used with discretion rather than something that is there all the time. My default is no vibrato.

Generally I only use it when playing jazz.

I have to say, I really like vibrato and would say that sometimes it is more natural to me than playing a note straight. Having said that I do use it alot more in jazz and some classical pieces. I've been told to steer clear when playing early music.

Agree with CJB on this subject, my default is to not use any (generally) unless i need it for tone colour in slow passages or warming long sustained notes.

It's not a technique i favour TBH i would far rather hear a pure warm centered sound made from a good instrument set up and a skilled players breath control and embouchure. I've heard too many players over the years use vib to cover up poor tuning and tone - so my brain automatically asks what they are hiding or covering up!! Sounding like Acker Bilk i don't find attractive any longer, it's like those warbling singers that make your ears bleed when you've listened to them for an hour or two.

Vibrato needs skilled and sparing use.

OK...

As a general rule, I'll avoid any use of vibrato for anything from the mid-Romantic period and backwards, otherwise I'll use it occasionally in later works (using the diaphragm usually), and more often than not I'll liberally use a jaw based vibrato for jazz works!

I've never tried it and my teacher has never suggested I try it.

I would only ever use it in jazz but I'm not a fan. Most of the clarinettists I've heard using it aren't supporting enough and it's accidental so I associate the two now.

Does practising vibrato from the diaphragm help to learn to support / control better? I mean, if you make a conscious effort to learn the different feel between greater or lesser support, does that strengthen your support control in general?
I like a little bit but I'm not massively keen on Gervase De Peyer's use for instance.

It can do, but it's not the way I'd choose to teach support.

I'm surprised to find so much antipathy to vibrato! Jack Brymer is nothing like so black and white in his book. And Acker Bilk is hardly typical of all jazz musicians, I would like to add - most of them are much more subtle.

Like most stylistic things, you use it as appropriate. I find a big vibrato on flute more offensive than on clarinet, for example, and don't even go there with Russian horn players (talking french horn not jazz here!)

This thread has been rather topical in my lessons recently. I need to get rid of my 'bad habit' of vibrato as all of my Grade 8 pieces don't require it, so, does anyone have any suggestions how NOT to play with vibrato and to keep the note straight. I think that I am using my lip to bend the note rather than my diaphragm.

It sounds like something you've picked up and ingrained into your playing, RAM. I'm also going to guess that you can play without vibrato : assuming that's the case, I'm afraid it's the good old 'p' word : practice, to get rid of it!

hahaha, this is my thread, LOL!

I use LOTS of vibrato and love a really big sound for clarinet. Just seems natural to me .... .

Never (yet?) encountered it.

Not surprised It's quite possible to not encounter it 'til grade 8 (or even beyond).