The 26-year-old defender collapsed while playing in a five-a-side game organised by the Angels at Hayesbrook School in Brook Street on Monday.
He was taken to Kings College Hospital in London by air ambulance and put on a life support machine but died the following afternoon.
Mr Slocombe, who had been playing for Crowborough Athletic, had previously collapsed while training or working out.
He had been fitted with a Reveal heart monitor to look for signs of arrhythmia (irregular heartbeat). It is understood that no abnormality had been detected.
James Folkes, the Angels defender who played with Mr Slocombe, tweeted: “Absolutely shocked and saddened to hear a former team mate @Char_Slocombe passed today after collapsing playing five a side.
‘Every young player starting out should automatic be heart-screened. It really should be a requirement when a club signs the player’
“As I previously said please all non league ballers get yourself checked out please… don’t need another casualty.”
He said: “My heart goes out to him and his family and I seriously urge all players to do it.. watching my friend Junior Dian collapse on the pitch was the worst experience of my life.”
Legendary former Angels striker Nathan Elder reiterated: “I can’t stress this enough. Get yourself checked out.”
Mick Payne, technical manager of the England amateur team, commented: “Every young player starting out should automatic be heart-screened.
“It really should be a requirement when a club signs the player. Databank will then be produced for all clubs.”
The Tonbridge club has a special affiliation with a charity called Cardiac Risk in the Young, or CRY, which campaigns for young athletes to undergo tests to discover any abnormalities in the heart.
It has carried out more than 1,100 heart screenings of young athletes aged between 14 and 35 at its Longmead Stadium over the past four years.
The Angels’ Football Fightback scheme was set up four years ago following the sudden death of two young players from previously undetected heart defects.
In 2015, triallist Junior Dian collapsed on the pitch and died during a game at Whyteleafe, aged 24. Seven years previously, Angels’ Under-18 player Jack Maddams, 17, died in his sleep.
Jack’s father Roger, a former chairman of the club, told the Times: “I was shocked to hear the news about Charlie. At Tonbridge Angels we feel it is vital that as many young people get screened.
‘They can either gain some peace of mind or get sufficient early warning where there may be cardiac issues so that steps can be taken to prevent tragedies’
“By doing so they can either gain some peace of mind or get sufficient early warning where there may be cardiac issues so that steps can be taken to prevent tragedies.
He added: “”At least 12 young people each week in the UK die of undetected heat issues. Cardiac screening should be routine for all in my opinion.
“Presently it is not – hence our efforts in recent years, raising awareness and positively making screening available. I would love to see more clubs take such steps.”
The Angels and the town’s residents have raised more than £35,000 to allow the testing to be carried out since 2016. The last session in January was fully booked up weeks in advance.
A screening session for 100 people costs £5,000, and Mr Maddams said: “We need to raise another £1,200 to fund our next day.
“In the meantime, I commend testmyheart.org.uk to anyone concerned about cardiac issues and the screening process.”
The club paid tribute to Mr Slocombe, saying: “Taken from us far too young, Charlie was a popular player at the club who was involved in both the Reserve and 1st team sides.
“He made of a total of 32 appearances for the 1st team and always showed a willingness to step up and help his team mates when required.
“It is known that he had a special affection for Longmead and all connected with the Angels.”
“Our thoughts are with Charlie’s family and friends as they try to come to terms with this devastating news.”
His father Keith said in a statement: “Everyone who met Chaz could see what a lovely chap he was and how proud he made me as a father.
“I’ve no words to say that can sum up what’s happened this last couple of days. RIP my son and best friend.”
To make a donation towards the screenings visit justgiving.com/FootballFightback