The driver of the busy rush-hour Croydon Tramlink service, which derailed near Sandilands tram stop shortly after 6.10am on Wednesday, has been arrested.
Theresa May said: "My thoughts and prayers are with all of those who've been affected by this terrible incident that has taken place on the tram in Croydon.
"Government is closely in touch with the emergency services and other authorities to ensure that all is being done that is necessary to deal with this terrible incident."
Emergency services spent hours freeing people trapped in the two-carriage vehicle while more than 50 people were taken to hospital, some with serious injuries.
Senior pastor at Croydon Vineyard church, Tom Thompson, told Premier: "It's a tram that many, many people in Croydon travel on regularly.
"I've been on it myself regularly with my children and know exactly the place where its happened, so, there's surprise and real sadness, I guess, for our town and particularly those who've been involved.
"It certainly feels like a moment when, as the people of God, we want to stand up and say: 'We recognise this as a moment that requires our solidarity with our community'."
Eight appliances and more than 70 firefighters were sent to the incident on Addiscombe Road which is thought to be the first crash involving fatalities on board since three people died when a tram caught fire in Glasgow in 1959.
Assistant priest at Our Lady of The Annunciation Addiscombe Catholic Church, Fr Keith Sylvia, told Premier: "People need a sympathetic ear, they need empathy, they need someone who perhaps can bring a different perspective to things and we are ready for people all the time, whether it's major or minor incidents in their lives.
"My prayer for all... those who have been injured is that, obviously, they find the right help and treatment they need... and also for those who have been bereaved that they would find comfort and strength for their families and their friends and all those who are professionals and ready to assist them at this time."
It appears the tram derailed at a point where the track branches, however an investigation into exactly what happened is now underway.
Croydon Health Services NHS Trust said: "Our staff are currently triaging and caring for them so we would ask members of the public with more minor routine ailments to consider going to the local walk-in centre or their GP if possible."
Mike Brown, London's Transport Commissioner, said: "All of our thoughts are with those who sadly lost their lives in this incident, those who were injured and the families of those affected.
"We are working closely with the emergency services on site and will continue to work with them during the investigation into what happened."
Finn Brennan, of the train drivers' union Aslef, said: "This is a tragedy for all those involved. For the women and men who set out this morning on their journey to work and suffered this awful accident and their families, the grief and pain must be terrible.
"There will be a full investigation into the causes of this incident by the RAIB (Rail Accident Investigation Branch) and others. There should be no rush to judgment or to place blame until the facts are known.
"For now, our thoughts are with all those injured and lost, their families, Tramlink staff and the emergency service and NHS staff working to save lives as they do every day."
Listen to senior pastor at Croydon Vineyard, Tom Thompson, speaking with Premier's Alex Williams:
Listen to assistant priest Fr Keith Sylvia from Addiscombe Catholic Church speaking with Premier's Alex Williams: