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Buy property in UK to open personal bank account

Buying a property is by itself not really an attractive enough proposition. You're just sending money in and sending money out. They don't make much money on that.

If you bring more to the table (keeping balance in the bank), you might be able to get an account.
Property is an answer to the question: what are your relationships with our country? (UK).
You can justify that you need UK bank account to receive funds from the tenant (which is true).

Regarding the balance, what kind of balance do you think they would be ok with?
 
In case person buys a small apartment in UK,
Would UK banks consider opening a personal account for non-resident and non-citizen?

Depends where you live. If your an Afghan or from Iran good luck. And if your an Afghan living in Iran then no bla-"!
 
If you're from outside the EU, you could try a Barclays UK International account for non-residents, but there's a minimum £25K balance, and you might need an introduction letter declaring good standing from a current bank of yours. If you're on this list it will be hard: https://www.ucl.ac.uk/research/site...ed_and_narrowly_restricted_countries_list.pdf

Wise is an alternative and would give you a UK sort code/account number.