@Cathryn - this is the tour series:
https://www.tourseries.co.uk/venues/ This is criterium road racing as a temporary circuit is built, whereas road racing is out on open roads. My son was doing the latter yesterday in the Seacroft Wheelers road race. Criteriums mostly happen on closed circuits rather than a temporary course due to the running cost. Road racing usually uses open roads with rolling road blocks or lead/follow cars.
There's lots of other races going on. British Cycling will have a list of local events and if you do a search then click 'More Filters' to filter it by 'Road race' in the Type of Event you'll work out what's going on near you in the future. They'll also get promoted on a British Cycling regional Facebook / Twitter group and looking at your location it'll be the South:
https://www.facebook.com/groups/637784002971311/ /
https://twitter.com/BCSouthRegion .
There's not that much near you except for Behind the Bikeshed's weekly series at Thruxton:
https://www.britishcycling.org.uk/events/details/237400/Behind-The-Bikesheds-Summer-Circuits-19 with others a bit further afield using Odd Down near Bath, or Alexandra Park in Portsmouth. There's also a road race on 22nd August in Shaftesbury (
https://www.britishcycling.org.uk/events/details/237386/John-Holman-Memorial-Race ) and the Junior Tour of the Mendips this weekend 13-15th August:
http://www.bristol-cycling.com/section.php/5/1/junior_tour_of_the_mendips - my son's team is taking part but he's racing in Northern Ireland in their Junior Series of Ireland this weekend. The other big event is the Tour of Britain in September, although this isn't near you:
https://www.tourofbritain.co.uk/stages/
The level of race depends on the type of licence required to take part. New racers have a 4th cat licence, progressing to 3rd cat (mine) then 2nd cat (my son's), 1st cat and Elite. The fastest races will be E/1/2 level:
https://www.britishcycling.org.uk/road/article/roadst_Road-Categories_Classifications but you'll see decent racing at all levels. Women's racing uses the same categories although a lady can race in a men's race one category lower.
Pretty much every team has Facebook and Instagram accounts; i.e. my son's team's Instagram is
https://www.instagram.com/jrc_shutt_ridley/?hl=en
They're based in Cheshire but there will be local teams near you. British Cycling's Clubfinder lists clubs and teams (shown as Club Commercial):
https://www.britishcycling.org.uk/clubfinder I
think your closest is the NoPinz team:
https://www.nopinz.com/2021/07/team-profile-nopinz-motip-race-team/
Hope that helps as a start. Racing's a minefield - even just road racing - without even stepping into the madness that's cyclocross
Or track, with Bournemouth near you having a velodrome.