Most clubs I have approached have always been a bit cagey about taster days with large groups of new people unfortunately, part of me does see the inherent risk in all fairness. I also seem to recall only a certain amount of days being allowed for non-member shooting a year (Maybe 28 or 30?) since one club I approached in November time had used up all their days, so couldn't legally offer me one (at least I was told).
For me the accessibility has a lot to do with affordability and the clubs culture.
If I add up the club membership and range fees I paid just to be a full member I am over £1000, which is not an affordable amount for many.
Many clubs, again in my experience, have been very cliquey and often don't offer the type of atmosphere that's opening to those wanting modern disciplines.
You only have to look at how many posts on here, other forums, and UK shooting subreddits there are about the difficulty of finding a club/range to see how hard it is for many to access, but I do get how in theory they should be pretty accessible if (like all things) they were ran efficiently and in line with HO rules.