A second man, also found with knife wounds, is being treated in hospital.
A 21-year-old man of Tower Hamlets, east London, has been arrested on suspicion of murder, the force said on Sunday.
He is being questioned and remains in custody.
BTP Detective Chief Inspector Paul Langley said: “We have been working around the clock to trace those responsible for his death and this is a positive step in the ongoing investigation.
“I’d like to thank the victim’s family for their patience and strength, and once again extend our deepest condolences to them.
“They are continuing to be supported by specially trained family liaison officers.
“I know the local community and many people across the country have been truly shocked by this senseless killing and we will continue to work tirelessly to make sure those responsible face justice.”