On past form, no they wouldn't.

http://www.bbc.co.uk/news/uk-england-london-10672343

More people are extradited from France to the UK than the other way round:

http://www.theyworkforyou.com/wrans/?id=2006-07-19c.83822.h

The greatest imbalances involving the UK are with Spain (far more are sent here) and Lithuania and the USA (far more are sent there - the US really does fit the image you're complaining of).

I can't find similar figures for Ireland. Maybe their system isn't sufficiently transparent for them to make them public.