Babcock’s would have essentially lost their ground as the company looked to reign in their commitment to Renfrew. They had their own bowling club, social club and sports grounds, but all of these have since been transferred to Renfrewshire council.
Moorcroft was the traditional local name of the ground, and Moorcroft played on for a number of years into the 21st century, at times fielding two teams in the Greater Glasgow and Scottish Amateur Leagues. Interestingly, and getting back on topic they retained membership of the Renfrewshire FA, so had semi-regular Renfrewshire cup semi-final appearances against St. Mirren and Morton. Presumably this membership was carried on from Babcock’s?
I’m not sure if Moorcroft are still on the go. Renfrew FC’s youth teams are among those who use the brand new 4G facility which sits where the grass football parks and cricket square lay. Ironically, Renfrew looked into moving to Moorcroft themselves before the establishment of New Western Park.