Only in a limited sense. The public did not have access to the land; specific "commoners" (local farmers) had specific usage rights e.g. for grazing.
1. a really dense network of rights of way – almost entirely on privately-owned land https://en.wikipedia.org/wiki/Rights_of_way_in_England_and_W...
2. open access to unimproved wild land: https://en.wikipedia.org/wiki/Freedom_to_roam#England_and_Wa...
The way this article reports the campaigners, you'd be forgiven for thinking that there are no existing rights of access in law, and for thinking that private ownership of land necessarily means absolute access restrictions.
This is not just a problem with this specific article; I've seen it numerous times, and it makes me think that this is a consistent pattern of this campaign; the campaigners are either wilfully ignoring the rights which already exist or are themselves woefully ignorant. Either way, they're doing the public a disservice by spreading what looks a lot like misinformation.