A $640 million cash bid by Toronto newspaper magnate Kenneth Thomson for control of Hudson's Bay Co. has been obersubscribed.

The Bay is Canada's largest merchandising chain with annual sales of about $2.6 billion.

Thomson heads a worldwide newspaper empire with more than 100 papers in North America and Britain, including the strike-bound Times of London.

Thomson won a bidding war agianst another Canadian giant, George Weston Ltd., for control of The Bay.

The fight for The Bay beganMarch 1 when the Thomson interest, through two private holding companies, offered $31 a share for a 51 percent interest in The Bay. Directors of the merchandising chain rejected the offer as too low in terms of assets and profit potential.

Weston has annual sales of more than $4 billion, controls the Loblaw and National Tea Co. supermarket chains, and is a major diversified food processor. It offered $40 a share in cash and stock for 51 percent of The Bay.*tThomson jumped its offer to $35 a share for a 60 percent stake. Weston also said it would take 60 percent but did not change other terms of its bid.

Thomson, the Second Lord Thomson of Fleet, decided to make a final shot at becoming a merchant prince as well. His group raised the bid to $37 for 75 percent and Weston capitulated. It advised Bay share-holders to accept the Thomson offer, and they did so in droves.

Thomson announced that about 89 percent of the issued Bay ordinary shares were tendered under the offer and that the stock would be taken up on a pro rata basis.

Both the Thomson and Weston bids were, studied by Canadian anti-combines officials but the federal government took no action to halt either bid. The concern with the Weston offer was that a combined Weston-Bay group would be the dominant merchandiser in Canada.

There also was concern that Thomson personally would control an interest of 60 percent of Canada's department store sales.

A newspaper controlling major advertisers could have serious anti-competitive effects, according to some sources.