According to good old Wiki, Longleat was the 1st drive through safari park outside of Africa in 1966 (though there had been a drive through - on a bus - lion exhibit in Tokyo 3 years before).
Then, in the UK, there was Windsor (1969), Woburn (1970), Blair Drummond (1970), Knowsley (1971), and Bewdley (West Midland Safari Park, 1973).
I think, to be able to remember it, I must have 1st gone to Longleat in 1969 or 1970 when I was 4/5. I still remember feeling quite scared at the prospect of our little car - a Morris Minor - amongst all the lions, but incredibly excited all the same.