Police believe the thieves targeted three properties in Barnet, northwest London, on Tuesday before breaking into Maureen Whale's home in Bells Hill just before 6pm.
They released images of jewellery stolen from the three properties, asking pawnbrokers or "handlers" of stolen goods to "do the right thing" and come forward.
Miss Whale, 77, a former air stewardess and nurse described by her family as "fiercely independent", called 999 after three suspects broke into her home, where she lived alone, and stole property, including her handbag.
As she was on the phone to the police operator Miss Whale collapsed. Police and paramedics rushed to her home and took her to hospital but she died the next morning.
Detective Chief Inspector Noel McHugh, of the Met's homicide and major crime command, said: "Everything we have heard indicates that Miss Whale was a wonderful lady, in touch with her family but living an independent life in the same home where she had been her entire life.
"We can only imagine how terrified she must have been to discover her home invaded and two men rifling through her possessions."
The burglars are believed to have started their spree earlier on Tuesday, entering the two other homes in Bells Hill via their rear balcony doors while the occupants were at work.
Detectives are also calling on people who work in bureau de changes to help them as about £30 of Turkish Lira and about £100 worth of euros were stolen from the two homes.
The break-in at Sampson Avenue happened through the rear patio doors and £200 to £300 in cash was stolen, as well as US$900.
DCI Hugh said: "I would appeal to any pawnbrokers or indeed any 'handlers' of stolen goods to consider the awful circumstances of what has happened to a wonderful elderly lady and do the right thing and come forward with any information.
"If you work in a bureau de change and someone has asked you to change those foreign currencies into sterling in the last few days we also want to hear from you."
He has also urged the public to help them apprehend the three suspects, describing one who entered Miss Whale's home as wearing a black zip-up gilet over a light coloured long-sleeved top with a dark beanie.
Another, who also entered the house, was wearing a long-sleeved top with dark patches, a hood - possibly with a fur trim - with dark trousers and light coloured trousers.
The third suspect acted as a look out at the window, and was wearing a long-sleeved dark hoodie with a baseball cap underneath the hood, light coloured tracksuit bottoms and dark trainers.
DCI McHugh is asking people who were in the area at about 5pm on Tuesday to hand over their dashcam and CCTV footage and let police know if there were any vehicles residents did not recognise in Bells Hills and surrounding roads.
Police have also asked two boys, aged about 12 and 14, who were seen on bikes in the area to get in touch as they spoke to the first officers on the scene and may be important witnesses.
"I would urge them to get in touch - if you are nervous about contacting police, speak to a teacher, parent or trusted adult but you are not in any trouble," DCI McHugh added.
He is also looking for somebody driving a small four-door hatchback car, possibly a Skoda Fabia, at 5.52pm up Bells Hills with the cemetery on their left, as they drove pas the suspects.
:: Anybody with information should contact police on 0208 785 8099 or call Crimestoppers anonymously on 0800 555 111.