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of course you can ask.......it was a very minor caution and fine from a magistrates court for 'Obstruction'.
basically, I'd had a drink and refused to move on from outside the pub when asked to do so by the police.
as the officer was in no mood for any cheek from a 20yr old lad, I was arrested.
I've spoken to others who have breach of the peace, and affray offences from fighting at football matches, and they were also issued visas, but had to wait 8 weeks.
For the US, drug offences are usually a no-go, and they're not too keen on drink-driving either (is anyone?), but unless it's a 'bad' crime, and depending how long ago, visas sem to get issued