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.
[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.
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.
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.