LONDON (AP) _ Lloyd's of London on Tuesday offered 21,000 hard-hit investors 900 million pounds or $1.34 billion to settle their claims for losses.

The investors, known as ''names,'' have until the end of January to vote on the deal, but groups representing large numbers of names said the offer was unacceptable.

Lloyd's total losses for 1990, the last year for which figures are available, were a record 2.9 billion pounds. For the years 1988-90 losses totalled 5.529 billion pounds.

The financial devastation at Lloyd's has bankrupted thousands of ''names'' who put their entire personal fortunes on the line to underwrite insurance policies at Lloyd's. In the Lloyd's insurance market, the names are grouped into syndicates that underwrite insurance polices.

''We think it's unacceptable and we're rejecting it,'' said Christopher Stockwell, chairman of the Lloyd's Names Associations' Working Party, representing 17,000 investors.

A series of disasters such as hurricanes, asbestosis claims and the Piper Alpha oil rig explosion is blamed for Lloyd's losses, but many names also allege mismanagement and lack of regulation within the market.

Members who accept LLoyd's offer will give up the right to bring legal action against Lloyd's for damages of any kind related to their participation in the syndicates.

Lloyd's chief executive Peter Middleton said more than 100 names would receive between 500,000 pounds and 750,000 pounds but fewer than 40 would get between 750,000 pounds and 1 million pounds.

He said the majority would receive less than 100,000 pounds.

John Mays, who represents almost 2,000 names, said the offer represented only about 10 percent of the names' losses.