LONDON, May 5— London telephones jangle to new numbers on Sunday, when city codes 71 and 81 replace the simple No. 1. If only it were that simple. ''I am totally confident that all the necessary adjustments will be made as planned on Sunday,'' said Millie Banerjee, general manager of British Telecom's London network.

She was speaking for the company, not the customer.

British Telecom is ready for as many as 50,000 misdialed calls a minute and has prepared recorded messages in the appropriate languages to intercept international calls placed with the wrong number. And in the Colonies. . . For international callers, London numbers will be preceded by the country code, 44, and either 71 or 81 depending on location in the city.

Callers within Britain will be dialing 071 or 081 instead of 01.

With Britain enjoying a three-day weekend, the real test will not come until Tuesday when banks, exchanges and businesses reopen.

British Telecom says London is the city that receives the most calls from the United States - up to 100,000 a day.

Because of the proliferation of fax machines and direct-dial business systems that assign a telephone number to every desk, the company said it had used up nearly all the potential five million numbers under the old London prefix. Splitting the city will double the pool. Geography and Status The 71 code has been assigned to inner London and the Docklands, and 81 to the outer reaches.

John Turner, British Telecom's communications manager for the code change, said Friday that as many as a quarter of the 380,000 businesses in London had not reprogrammed their telephones or fax machines.

David Fletcher, chief executive of the British Security Industry Association, estimated that a fourth of the capital's 100,000 burglar alarms had not been adjusted to contact the new numbers.

Some people are upset by the change for other reasons. They believe that self-esteem and property values will decline in areas with the 81 code like Finchley, Hornsey, Shepherd's Bush, Hammersmith, Wembley, Putney and Tooting.

Elsie Burch Donald, author of ''Debrett's Etiquette and Modern Manners,'' laid down the law a year ago: ''071 will be a superior number to have,'' she wrote. ''Clearly there is an advantage socially, culturally, economically to be living in central London.''