The man had a medical emergency on Wednesday
The 52-year-old entered the newsagents in St Nicholas Avenue on Monday, 3o December at around 6.50am with a knife and started threatening staff with the weapon.
The armed robbery suspect was detained by staff and a member of the public.
Prior to officers arriving, the man suffered a medical emergency.
He was taken to hospital in a critical condition but died on Wednesday, 1 January.
A special post mortem will take place in due course.
His next of kin has been informed and will be supported by specialist officers.
A spokesperson for the Met Police said: “An investigation into the death is taking place as is common practice for all unexplained deaths.”