"I am preferring to" sounds outdated to me, I haven't heard it spoken by any of my fellow Brits for a very long time. Can you show us a link to "the Cambridge?"

You have not worded your question very well. You have mislead us to think the dictionary said "I am preferring to ----(x)" that is incorrect. "I prefer + (verb+ing)" is acceptable. "I am preferring to --(x)" = A long time ago some people spoke like that in specific circles I think it was "the legal profession".

I can't imagine losing points on the IELTS on a basic, widely accepted structure. Unit 59 of English Grammar in Use by Murphy clearly gives both forms as standard. [excerpt] You can use 'prefer to (do)' or 'prefer -ing' to say what you prefer in general. I don't like cities. I prefer to live in the country. or I prefer living in the country. I prefer driving to travelling by train. I prefer to drive than than travel by train. I suspect your teacher can't support his statement. I did Google Ngrams for "prefer to eat/prefer eating" and "prefer to drive/prefer driving." The "prefer to (do)" form is more common in print. https://books.google.com/ngrams/graph?content=prefer+to+drive%2Cprefer+driving&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cprefer%20to%20drive%3B%2Cc0%3B.t1%3B%2Cprefer%20driving%3B%2Cc0 https://books.google.com/ngrams/graph?content=prefer+to+eat%2Cprefer+eating&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cprefer%20to%20eat%3B%2Cc0%3B.t1%3B%2Cprefer%20eating%3B%2Cc0

"preferring to be alone" Headline dated March 1Oth 2018. http://www.wroolie.co.uk/2018/03/preferring-to-be-alone/ I knew I had come across this structure, but this is subtly different to your question. I also have heard people confuse this structure with "I prefer being alone" and "I prefer to be alone" and as a result say strange sentences. "Preferring to be + somewhere else/ alone/ with friends/ on holiday" is describing the persons preference" "I am" is not used in these situations.

Now the question makes sense. With the edit the examples and the links. "prefer to" or "prefer + verb-ing". Yes you can use either.