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Tea drinking and drinking tea are both phrases that refer to the custom of consuming a beverage made by immersing the leaves of certain plants in hot water. The gerund drinking fits equally well before or after tea.

Tea drunk uses the past participle of drink to refer to tea that has been consumed.

For example:

Tea drinking (or drinking tea) is widely recognised as bringing health benefits.

and

The amount of tea drunk has increased since its health benefits were recognised.

Thus the first of your examples is correct. The second is not.

It's not grammatical to say that tea drunk is a British custom.

Yes, you can begin a sentence with tea drunk:

Tea drunk without sugar is better for you.

meaning that tea consumed without sugar is better for you.

Equally, you might write:

Drinking tea without sugar is better for you.

whereas to write

Tea drinking without sugar is better for you

is NOT idiomatic.

"Tea drunk" is not an idiom, and only makes sense with the meaning "[some] tea [which has been] drunk".

"Tea drinking" is a noun phrase, and its head is the verbal noun (gerund) "drinking". I would be inclined to hyphenate it ("tea-drinking").

"Drinking tea" is a full non-finite clause, which still has verbal qualities. For example, you can modify it with an adverb ("slowly drinking tea"), or elaborate the object ("drinking several cups of very hot tea").

"Tea-drinking" is a noun phrase where most of the verbal qualities have been leached out, so you can't do those things.

There is another use of the phrase "tea drunk", which has its origins in Chinese, as 茶醉 (cha zui, which literally translates to "tea drunk"). It's a state of being, named because it's similar to being drunk on alcohol, with symptoms including dizziness, weakness, and nausea. In this case, "drunk" is a noun and "tea" is an adjective specifying the type of drunkenness, similar to phrases such as "wine drunk" or "liquor drunk."

Example B would still not be correct with this interpretation, as it's not an activity that can be a custom. However, one could say something like "If you drink tea too quickly, you could get tea drunk."

Usable patterns:

• Drinking tea is nice.


• Tea drinking is a custom in some countries.


• Answering questions is difficult.


• Playing tennis is boring.

Tea drinking is subject matter. Drinking tea is the actual activity.

All those are activities. In English, we use gerunds as nouns all the time. Here they are all the subject of the sentences I have provided. Knowing that might be helpful to you. In this last case, "knowing that" is the subject made up of a non-action verb that can take a direct object.

Drinking too much is not good for you. [drinking, as in drinking alcohol]
Drinking wine with friends can be amusing.

Another usable pattern, past participle + prepositional phrase, used adjectivally:
The tea ||drunk at the gathering|| was from Japan.
The movie ||viewed at the conference|| was terrible.
The man ||seen on the bus|| was the spy.

Drank and Drunk: Past Tenses of Drink

You asked which of the following was the preferred way of expressing the custom:

A: Tea drinking is a British custom

B: Tea drunk is a British custom

A is correct, because "tea drinking" is a compound word of the form noun plus gerund that forms a single subject for the sentence. Stereotypes aside, you can think of the sentence as:

[The act/practice of] tea drinking is a British custom.

or, alternatively:

[The act/practice of] drinking tea is a British custom.

In the sentence B, "drunk" is an arguably-ambiguous form of the past participle of the verb drink. In casual speech, at least in America, people will often use drunk and drank interchangeably, although "drunk" can also be used as a noun or adjective for being inebriated. As a result, it is often better (at least in formal speech where you're attempting to avoid negative connotations or ambiguous parsing) to say "drank" instead.

Because tea drinking isn't describing something that occurred only in the past, B should be rejected because the past tense of the subject doesn't align with the tense of the verb is (the 3rd person singular present indicative of be). Grammar rules aside, it also just sounds wrong to an American English speaker like me.

Examples

Some examples of where drank would be an appropriate word choice would be:

I drank a lot of tea this afternoon. [simple past]

The American guests have drank almost as much tea as their British hosts at the party tonight. [past participle]

As both terms also form the past tense of drink, in informal speech you might also hear:

All the tea in the house was drunk this afternoon.

All the tea in the house got drunk this afternoon.

Despite the ambiguous or ungrammatical word choices, these informal sentences would be understood as the past tense of drink because the subject (the tea) couldn't possibly be (or become) inebriated.

However, to the educated American ear, a sentence like I drunk all the tea. would sound wrong even if drunk were a legitimate past tense of drink. For that reason, I'd recommend using drank as the past tense, although you may certainly hear drunk used the same way informally.

Dictionary Sources

In American English, drank is both the past tense and the past participle of drink, whereas drunk can only ever be the past participle. So, as a purely pragmatic issue, drank is much more likely to used correctly.

For reference, see https://www.merriam-webster.com/dictionary/drank and https://www.merriam-webster.com/dictionary/drunk. Other regions and dialects may vary.