The following snippet from Wikipedia doesn't fully answer your question, but it's at least suggestive of what might have happened: the UK standardized the tablespoon as a volume measure using its “eating spoon” meaning while Australia used its “serving spoon” meaning. Before about 1700, people generally brought their own spoons to the table.
Spoons were carried as personal property in much the same way as people today carry wallets, key rings, etc.
From about 1700 the place setting became popular, and with it the "table-spoon," "table-fork," and "table-knife.
" The 18th century witnessed a proliferation of different sorts of spoons, including the tea-spoon, coffee-spoon, dessert-spoon, and soup-spoon.
In the UK, the dessert-spoon and soup-spoon began to displace the table-spoon as the primary implement for eating from a bowl, at which point the name "table-spoon" took on a secondary meaning as a much larger serving spoon.
At the time the first edition of the Oxford English Dictionary was published, "tablespoon" (which by then was no longer hyphenated) still had two definitions in the UK: the original definition (eating spoon) and the new definition (serving spoon) .
By the time of the second edition, the first definition was relegated to "also, occasionally".
However the term "tablespoon" referring to a serving spoon has been on the decline in the UK since cooking books became common; it has more and more been used the same way as in the USA due to the measurement system outlined below.
Source:
http://en.wikipedia.org/wiki/Tablespoon
Here's a list of the definition of the tablespoon measure from older recipe books published in different English-speaking countries.
It's a short list, but it does somewhat show that the Australian definition evolved to be generally higher (20ml-25ml) than the UK one (around 18ml), with the South African one on the lower end (12.5ml).
Margaret Powell (British)
1970 Tablespoon = 18 ml Australian and New Zealand
Complete cooking 1973 =
Tablespoon =
25 ml Best of Cooking (Hamlyn)
- Tablespoon, (Australia) =
20 ml Best of Cooking (Hamlyn
) - Tablespoon, (British) = 17,7 ml Best of Cooking (Hamlyn)
- Tablespoon, (America) 14,2 Indian Cooking, Chowhary 1952 -
= Tablespoon = 25 ml Cook and Enjoy, De Villiers 1971 (South Africa) =
Tablespoon =
12,5
ml Complete South African Cookbook (South Africa)
1979 Tablespoon =
12,5
The Australian Women's weekly 1978 =
20 ml Source: http://whitegranny.blogspot.com/2008/11/beware-of-tablespoon.html
The proliferation of spoons mentioned in the Wikipedia snippet above is still evident in recipe books today.
British recipes occasionally still use a “ dessertspoon ” to mean a 10ml measure.
In Dutch recipes (link to a page in Dutch), a 5ml measure is referred to as a “coffeespoon,” while a “teaspoon” refers to a 3ml measure.
cooking.stackexchange.com/users/4012/Rinzwind
I would basically ignore it.
Domestic recipes are generally never that accurate anyway.
Does the recipe mention level or heaped tablespoons?
Does it say 20 ml for a tablespoon?
For rising agents you may want to be a little more accurate, so how about 1 tablespoon and one teaspoon, or just 4 teaspoons, or even just heap it a little?
I have a few Australian published recipes with dual measurements, and they show tablespoon as 15 ml, so the whole 20 ml thing may not be so universal in Australia in more recent times.
Some examples are: Smoked Loin Roast Beef Stroganoff II
Many Australians are recent immigrants, including 500,000+ from New Zealand and they all use 15 ml tablespoons Another issue being that now all the basic kitchen utensils are made in China, so they get what every one else gets, 15 ml
In the history of the tablespoon it has meant many different sizes in many different cultures, from South Africa with 12.5 ml, to India with 25 ml
cooking.stackexchange.com/users/3203/TFD
I still have the booklet issued to all Australian households by the Government when Australia adopted metric measurements.
The standard adopted by the Australian Government for one tablespoon is 20 ml.
The reason given was that the Australian tablespoon had always been larger than 15 ml, at a fraction under 18 ml, and so 20 ml was the closest
measurement.(It was recognised that in the UK, USA, and NZ, a tablespoon was around 15 ml.)
So now, because most such things in stores are mass-produced overseas for world-wide markets, almost all available tablespoons, at 15 ml, are not of the Australian Metric Standard.
cooking.stackexchange.com/users/65409/George Senior
Back in history, a tablespoon was what you might call a serving spoon nowadays, perhaps 20ml-30ml, and teaspoons were more like 7ml-8ml.
In these parts, old style teaspoons are still common.
Somewhere in the 1960s, in an effort to prevent people having problems with medicinal doses, teaspoons were standardised to 5ml and tablespoons to 15ml in the US and Europe.
Australia has standardised the tablespoon to something that reflects the old usage, although my mother's idea of a tablespoon was actually more like 25ml.
It is like those old recipes where a "cup" turns out to be 6 fluid oz ...
cooking.stackexchange.com/users/5885/klypos
A 15mL tablespoon is three 5mL teaspoons.
The Australian tablespoon would just be four instead of three.
Equivalently, that would be one 15mL tablespoon plus one 5mL teaspoon.
cooking.stackexchange.com/users/4489/Ray
In Australia, a tablespoon is defined as four teaspoons, equaling to 20 ml (0.68 US fl oz).
In writing volume-based recipes, an abbreviation like tbsp.
is usually used to refer to a tablespoon, to differentiate it from the smaller teaspoon (tsp.).
cooking.stackexchange.com/users/69542/Laila
In Australia, a tablespoon is defined as 20mL whereas it is 15mL in nearly all other countries.  I'm interested to know where this comes from, and also what other Australian people do about this because the shops here seem to favour the 15mL variety which isn't a whole lot of use for local recipes.
Why is a tablespoon defined as 20mL in Australia?
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cooking.stackexchange.com/users/5833/Flash
This is partly because table spoons were different sizes in different countries, and cooking recipies were not very exact in the past. A tablespoon measurement in Australia was initially defined as four 5ml teaspoons, but now most utensils are mass produced abroad and people tend to use the same measurements as in other countries. It goes back to the standardization of measurements. Every country used a slightly different measurement but now that cutlery is mass produced, they just use 15ml as that is used in most places.
The tablespoon goes back to when cutlery was first being used on tables. Australia took a different standardization to other countries.  Because most things are mass produced in China, 15ml is what you find the most of in Australia. Just use 4 teaspoons instead of a tablespoon or reduce the quantity slightly. Home recipes are never that exact anyway.