Did somebody mention telephones?
The U.K. numbering system is certainly not the easiest to comprehend until you are familiar with it, although in many ways it's actually a lot simpler now than it was 20 years ago. Back then there were still small villages with 3-digit local numbers, and a single town could have a mixture of 4-, 5-, and 6-digit local numbers.
Let's start with the initial zero of an area code. Although technically it is a trunk prefix, it is always written here as though it is an integral part of the area code itself, unlike the "1" in North America which is written separately or omitted altogether.
The "official" method for writing a full number in Britain is to enclose the area code in parentheses, or to separate it from the rest of the number with a space or dash, e.g. (01234) 567890 or 01234-567890.
In most parts of Britain outside the large urban areas, the area code takes the form 01xyz, where "x" is any digit 2 through 9, "y" is any digit except 1, and "z" is any digit. The full list of these codes runs into the hundreds, but here are a few examples:
01752 Plymouth
01224 Aberdeen
01273 Brighton
01332 Derby
01603 Norwich
The local numbers in these areas are then 6-digits long, and it is the convention to write the number as a continuous block of six digits. The first two or three digits of the local number identify the actual exchange within the area. For example, within my area code of 01692 (North Walsham) if the first two digits of the local number are 58 then it is a Stalham number. 59 is Hickling, 63 is Horning, and so on. I'm on Stalham exchange, so my number is 01692-58xxxx.
Aside from London, several of the other major cities have used 7-digit local numbers for many decades. These have the following area codes:
0121 Birmingham
0131 Edinburgh
0141 Glasgow
0151 Liverpool
0161 Manchester
0191 Newcastle (this being a more modern addition).
The 7-digit local numbers are written in the more familiar xxx-xxxx form, and as in America the first three digits then identify the actual exchange within the area.
Note that in all of the above examples the first "1" of the area code has only been in these codes since 1995, so if you were looking at old ads (or even some signs still in use) you would see Plymouth as 0752 and Liverpool as 051, for example.
In the last few years several other cities have moved up to 7-digit local numbers and have had new area codes of the form 011x assigned. These are:
0113 Leeds
0114 Sheffield
0115 Nottingham
0116 Leicester
0117 Bristol
0118 Reading
So a current Reading number, for example, would be shown as (0118) xxx-xxxx, or possibly 0118-xxx xxxx.
One of the most recent changes in the numbering system is the adoption of 8-digit local numbers in some areas. These areas have an area code of the form 02x, thus:
020 London
023 Portsmouth / Southampton
024 Coventry
028 Northern Ireland
029 Cardiff
The recommended form for the 8-digit local number is for it to be written as two groups of four, e.g. 2345-6789.
In all cases, if you are calling a number within the same area code as your own, then you need dial only the 6, 7, or 8 digits of the local number. There is no mandatory dialing of the area code even if it's the same as your own as exists in a few parts of the States now.
"Area" codes starting with anything other than 01 or 02 are non-geographic codes. 0800 and 0808, for example, are toll-free numbers, broadly equivalent to American 800/888 etc. numbers. There are dozens of other special codes which would take another full post to explain, but as mentioned already, cellphones have their own special area codes here, in the 07xx group. Thus when calling from a cellphone to a landline, or vice versa, you will
always need to dial the full number including area code.
When calling into the U.K. from overseas, you must use the international prefix for whatever country you are in, followed by the U.K.'s country code 44, followed by the full area code and number,
however, you must drop the initial zero from the area code. The international convention for writing a number is to use a plus sign to show that the country-specific international prefix must be used. Here's an example of how a number would be written in U.K. and international formats:
U.K. (01234) 567890
Int. +44 1234 567890
The prefix you substitute for the "+" depends upon where you are calling
from (011 for the U.S. & Canada).