Prime Minister David Cameron has led tributes ahead of the Westminster service, saying people "must never, ever forget what happened".
The massacre was the worst in Europe since World War Two.
It came amid the bloody break-up of Yugoslavia into independent states.
Serbia backed Bosnian Serb forces fighting the Muslim-led Bosnian government during the conflict.
In July 1995, in what was supposed to have been a UN safe haven, Bosnian Serb forces took control of Srebrenica. They rounded up and killed the men and boys and buried them in mass graves.
A commemorative event will also be held on Wednesday in Cardiff, hosted by First Minister of Wales Carwyn Jones.
Scotland`s First Minister Nicola Sturgeon will host a memorial service at St Giles` Cathedral in Edinburgh, on Friday.
The Princess Royal will travel to Bosnia and Herzegovina on Saturday for Srebrenica Memorial Day.
People gathered at Belfast City Hall on Sunday to mark the start of Srebrenica Memorial Week.
About 2,000 invited guests at Monday`s hour-long service in Westminster Abbey, will witness candles being lit in memory of those killed.
They will also hear Munira Subasic, president of the Mothers of Srebrenica association, tell her story.
`Agony continues`
The service, which began at 12:00 BST was organised by the UK charitable initiative Remembering Srebrenica, and will be followed by a reception hosted by David Cameron at 10 Downing Street.
There will also be a formal reception in the Houses of Parliament hosted by Speaker of the House John Bercow.
Mr Cameron said: "We must never, ever forget what happened".
"The 20th anniversary is a moment to remember the many thousands who lost their lives, to remember their families and the missing, and the fact that for so many - including the Mothers of Srebrenica - the agony continues every day, undimmed by the passage of time.
"We must reaffirm our determination to act to prevent genocide in the future."
Lord Ashdown, who became the European Union`s High Representative for Bosnia and Herzegovina in 2002, will tell the Abbey: "Whether through error, misjudgment, an inability to comprehend, or just inattention, we stood aside when we should not have done.
"We should therefore remember Srebrenica, not just to bear witness to those who suffered, but also as a warning to us all of what happens when we turn our back."
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