Amanda Foreman explains:
Thatcher’s handbag, at first a symbol of weakness, had become a thing of unparalleled power. “The men I talked to about Thatcher,” says Streep, “claimed when she reached for the bag, you just never knew what was going to come out. Your heart went into your feet.” At one cabinet meeting the ministers arrived to find her absent but the iconic article sitting on the table. “Why don’t we start,” suggested the environment secretary. “The handbag is here.” The handbag became her leitmotif, marking her out as a prime minister who was part Lady Bracknell and part Winston Churchill.
A history of the Iron Lady's accoutrements:
Her pocketbooks came to be viewed as veritable munitions depots constructed of polished black leather. They became a synecdoche for the woman herself: conservative, intimidating, feminine. (An Asprey bag that belonged to her sold this summer at auction for about $39,000.) Thatcher didn’t need to wield a gavel. She could place her bag on the table to announce her presence. This swaggering announcement of womanhood was a way to consume space and demand attention. It marked her territory. To be sideswiped by Thatcher was to be "handbagged."