Valid B2 US visa on Polish passport vs ESTA

Hello All,

I am travelling to US in October 2018 . I have a B2 visa ( valid until 2025) on my Polish passport, which will expiry in January 2019, which by the time I arrive in US , there will be only 3 months left on it , and I am sure they will not even let me board the plane with it.
I have now British Passport which I would like to use instead for this journey and I understand I will need apply for ESTA.
My question is , can I apply for ESTA , even though I have valid B2 visa on different passport under the same name , or do I should apply for a new Polish passport?

Please help.

Ange

If the purpose of your travel to the US is a short holidays they will let you board the plane with that B2 visa on your Polish passport and you will be allowed to enter the US normally.

If you prefer to enter the US on your UK passport then simply apply for an ESTA and you will be fine as well.