But the gallery said it collected items of "outstanding aesthetic or technical quality" rather than garments with "social historical value".
More than 300 items will now be sold at auction next month instead. Lady Thatcher died two and a half years ago.
She was the longest-serving premier of the 20th Century and Britain`s only female prime minister to date.
The clothes to be auctioned by Christie`s include her blue velvet wedding dress and various power suits worn during her tenure in Downing Street, plus handbags and jewellery.
A spokesperson for the museum told: "The V&A politely declined the offer of Baroness Thatcher`s clothes, feeling that these records of Britain`s political history were best suited to another collection which would focus on their intrinsic social historical value.
"The museum is responsible for chronicling fashionable dress and its collecting policy tends to focus on acquiring examples of outstanding aesthetic or technical quality."
In recent years the museum, which described itself as "the world`s leading museum of art and design", has put on crowd-pleasing shows of fashion by designer Alexander McQueen and clothes worn by pop legend David Bowie.
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