Yes, there is — everyone is welcome, including absolute beginners. There are classes and activities for different levels of learning, including for young children too. We also always have traditional dancing and singing and a guided walk to local places of interest with commentary in both Kernewek and English. It’s lots of fun and I’ve met so many nice people there. It would be lovely if you could come too some time! 
(There’s another discussion about it here: Cornish Language Weekend - #20 by Courtenay - Other Languages - SSi Forum)
Yes, you’re right — it’s officially a county of England, even though it’s no more “English” than Wales or Scotland or Ireland. 
You can actually feel the difference as soon as you cross the River Tamar, the border between Devon and Cornwall — partly because almost all the place names are suddenly Cornish instead of English, but the culture is different too. It’s really unique and most Cornish people want to keep it that way and not be thought of as just another “part of England”, which truly it’s not.
(I’m Australian, by the way, and I live near London now, but my ancestors on my father’s side were Cornish and I just love Cornwall — that’s why I’m learning the language. Some parts of Cornwall actually remind me of Australia! I think it’s the magnificent coastline and the fact that the climate is generally a bit warmer there, so they can grow a lot of the kinds of plants we have in Australia too.)
I don’t know the history that well — I know there were active efforts to stop Welsh people speaking Welsh (children being punished in school if they spoke Welsh and so on). In Cornwall, I think it was more that English gradually took over from Kernewek and became the language everyone most “needed” to speak, while Kernewek was thought of as a “peasant” language that only uneducated people spoke.
You probably know that Kernewek almost completely died out — the last few fluent speakers died in the 1780s and '90s, and while there were always a few people who remembered some old sayings and poems and phrases that had been passed down the generations, Kernewek wasn’t revived again as a spoken language until the early 1900s. It’s become stronger since then, but still fewer than 1000 people can speak it fluently and there is nowhere in Cornwall where you can find a whole community of people speaking Kernewek as their everyday language. But maybe that could change some day (maybe)…