Best place for up-to-date info is definitely their Facebook page: https://www.facebook.com/beckenhamplacepark/
As soon as the golf course officially closed the dog walkers colonised it! Casual golfers have returned to use the course while it's still there, but keeping getting their balls nicked by opportunistic dogs! Where the dog walkers go, everyone else soon follows.
Work is still at an early stage. Mostly clearing and replanting, although there is definitely digger activity where the lakes / wetland area is planned.
I've noticed the woodland is being better managed in a housekeeping sort of way - bins being emptied more regularly, and a maintenance guy riding round in a golf buggy. Paths have been mowed into the fields, but the rest left to go to meadow, which is lovely at this time of year.