It’s surprising how many new vineyards pop up every year it seems. The advantage of a discussion such as this is that local knowledge is often needed and can be tapped into.
I live in Hampshire, which is towards the western end of the main southern vineyard area. There’s a big(-ish) one in the next village along. Waitrose, and increasingly M&S - plus local independents usually carry a range of the more local ones. Plus some from the surrounding counties. Those from further afield are harder to source without sending away for them, so I’m not too well up on, say, Kent, where I am aware there is an active winemaking scene.
So far as Hampshire vineyards are concerned, most are members of Vineyards of Hampshire who have a website, so you can look them up here -
Vineyards of Hampshire - link
Of these, probably the best known are Hambledon (the society often carries their NV, though none at present), Hattingley Valley and Exton Park.
Hattingley Valley is a big operation and well worth a visit if you get the chance - they do contract winemaking for sparklers from around 10-12 other estates. HV is Britain’s biggest exporter of sparkling wines to the USA, and also produces the wines for Pommery’s English sparkler. Emma Rice, the head winemaker is an entertaining and affable host if you can get one of their extended winery visits. Their website is worth a look, especially for the “management lunch” picture in the style of the mad hatter’s tea party!
Hambledon is famous for being the first vineyard in England to plant wine grapes in the 20th century (or so they claim), but this was for still wines, and they were all grubbed up in favour of the classic champagne grapes. This is another sizeable operation. Hambledon is currently building a big visitors centre (bigger than their existing one) which should be finished very soon I think - also well worth the visit for a tour of both the vineyards and production.
Exton Park is another quality-oriented producer of sparkling wines - they often do a single meunier which does well here. Winemaker is Corinne Seely, who is the wife of Christian Seeley , MD of AXA Millesimes, who own more classical wine estates than you could shake a stick at.
Jenkyn Place make a good range of sparklers, slightly different as (I suspect) their vineyards are on greensand over chalk, which would make them more like (most of) their Sussex brethren. Winemaker is Dermot Sugrue at Wiston.
Cottonworth and Black Chalk up in the upper Test Valley are very good, and Waitrose’s own sparkler comes from here too. (Nyetimber has a large block of mostly chardonnay on the chalk here).
Danebury make both still and sparkling wines (M&S often have them), working mostly with non-classic grape varieties, though they seem to have been reeling in a number of prizes of late for their still wines, so maybe worth a look if you are after those.
I don’t know a lot about most of the rest, though such as I have tried would suggest the standard is high. After a slightly wobbly start, Raimes are now good. Of others worth trying and not members of Vineyards of Hampshire, the still Pinot Noir and the Bacchus from Titchfield Vineyards are good. Christian Seeley’s own sparklers from Coates and Seeley are good, but hard to find for some reason - maybe he exports them? Waitrose’s own sparkler is from their estate in the Test Valley and is reliably good.
No doubt there are others, though that should be enough for now I hope!