Thanks! I called the council on Friday morning and they said it was NOT going to be free.
I last checked the news section of their site on Friday afternoon, and nothing had been published on this. It seems they communicated it at the very last moment.

I wonder if the parking app was updated to reflect this or not!

It appears no charge: http://www.wandsworth.gov.uk/news/article/14484/free_parking_on_bank_holiday_monday

Will parking in controlled parking zones in Wandsorth be free on the two May bank holiday Mondays? I'd guess no because I haven't found anything on the council's website, but I was wondering if anyone knows for sure?

I have also tried to call the council on the number at http://www.wandsworth.gov.uk/info/200459/parking_zones/218/parking_zones/10 , but no one ever picks up.

AFAIK parking is free in controlled-parking zones in Wandsorth on Easter Monday, and the council always publishes a news update on its website confirming as much, e.g. http://www.wandsworth.gov.uk/news/article/14457/free_parking_on_easter_bank_holidays

However, the only year for which I have found some confirmation that parking was free on the May bank holidays was 2014: http://www.wandsworth.gov.uk/news/article/12322/how_to_avoid_a_bank_holiday_parking_ticket