The area code for all of London is 020, which is +44 20 in international format.
(The plus sign means "insert your international access prefix here." From a GSM mobile phone, you can enter the number in full international format, starting with the plus sign. The most common prefix is 00, but North America (USA, Canada, etc.) uses 011, and many other countries use different prefixes.)
Peckham
peckham
Peckham is an area of London not an estate. Nelson Mandela House was on the Nyerere estate.
This isn't a London code. It is the area code for Brentwood in Essex which is about 30 miles northeast of London.
East London covers a large area so it all depends on which part of East London and your method of transport. Anything between 20 minutes and 3 hours if you are walking.
In the UK, telephone area code 020 is London. A number beginning with 020 3432 is a "virtual" number that could be anywhere in London. Furthermore, with number portability any specific 020 number could be located anywhere in the London area, served by any local phone company.
The London phone directory no longer lists London telephone areas. All that can be gleaned from the given number is that 020 means that it is a London number and 8578 is somewhere in the outer London area.
In the UK, area code 020 is London, but there are no numbers beginning with 020 2. Other countries may have similar telephone area codes.
UK telephone area code 020 is London and surrounding areas. It is not possible to narrow down the location any further with the information given. Furthermore, with number portability, any specific 020 number could be located anywhere in the greater London 020 area.
London's telephone code is 020 followed by an eight digit number which will start with 3,7 or 8. The number that you have asked about is not a London number as you have described it.
UK telephone area code 020 is greater London. A number beginning with 020 8262 could be located anywhere in the greater London 020 area; that prefix is not associated with any particular borough, district, or neighbourhood. Furthermore, with number portability, any 020 number could be located anywhere in greater London, served by any local telephone company.
020 is London. 020-3 numbers can be anywhere in London. The operator who "owns" this number is Frontier Systems. Note that the area code for London is just 020, not 0203 or 0207 or 0208.