"Not a clue" vs. "no clue"

Example:

• — What is he called?
  — I have not a clue.

• — What is he called?
  — I have no clue.

Are both versions grammatical in English? If they are, which one is preferred by native speakers in the US and the UK?

Solution 1:

In British print sources, the answer to this question changed midway through the 20th century. Before 1945, “I have no clue” was nearly always preferred to “I have not a clue”. Beginning that year, “I have not a clue” and “I haven’t a clue” began a sharp rise in popularity,¹ dominating by 1980.

American print sources exhibit virtually the same pattern.

Notes

¹ Google Ngram Viewer does not differentiate not and n’t. There is no way to chart the two separately.

Solution 2:

As an Englishman who has lived in the US also, out of the two it's 'I have no clue'

Personally I'd prefer 'I'm clueless' probably because it has less syllables.

In the past tense you would say 'I didn't have a clue' or my favourite would be 'I was clueless'

And looking forward you would say 'I wouldn't have a clue' or my favourite 'I'd be clueless'