Jack Favell's facetious suggestion that they should try 'every exchange in London' would certainly have been a tall order! By 1934, the London telephone area had 147 exchanges within 12.5 miles of Oxford Circus, each of which was represented by a code related to its location.
For example, the code for the Abbey exchange (serving Westminster) was ABB; the code for the Hampstead exchange (serving Hampstead) was HAM; the code for the Museum exchange (serving Bloomsbury) was MUS; the code for the Mayfair exchange (serving Mayfair) was MAY; the code for the Trafalgar exchange (serving Whitehall) was TRA; the code for the Wimbledon exchange (serving Wimbledon) was WIM. Telephone subscribers were given 7 digit numbers which included the exchange code, plus 4 further numbers; for example WIM 0576; HAM 1024. This system came to end in 1966, by which time there were 350 exchanges, and the possible code permutations to represent them had been exhausted.
When London is phoned from Manderley, the call has to be connected by an operator. However, in London itself, from 1927 onwards, calls to other London exchanges could be dialled directly using the Director System. Each number on the telephone dial (except 1) represented letters of the alphabet: 2 for ABC; 3 for DEF; 4 for GHI; and so on, to 9 which represented WXY. So, if a Londoner wished to phone a fellow Londoner at the number WIM 0128, they would dial 946 0128. Callers from outside London would simply ask the operator for Wimbledon 0128, just like Frank asks the operator for Mayfair 0488.