Bank account budapest

Hi

I want to set up a current account as I'm looking to buy a property in Budapest to rent out. However, are there any banks that will open a current account without a residence permit?
Opening the account without the permit would probably be easiest.

Or how easy is it to obtain a residence permit for a UK citizen?

Kind regards
Mark

I found  both of these things very easy and some uk banks have overseas links . message me if you want any further information . I did some things the hard way but I have worked out better ways as I have gone along .
The one drawback is that my hungarian bank has charges just for having an account so I tend to use my uk account for most things . regards Anns