Italian Citizen to marry a Mexican in UK?

Hello everyone, I am Italian and I live and work in Northern Ireland. I have been dating this girl for quite sometime now and we have decided to get marry and live together.

Now, because my country is still suffering from a huge economic crisis, I would prefer to stick and live here in UK, however my question is, can I marry my gf here in the UK or does it needs to be done back home in Italy?

I don't have any issue whatsoever of marrying her in Italy, but what I care about is to bring her with me in the UK after married.

Could anyone give me an idea of how this works?

Thanks

You can get married in the uk without a problem. Once you do marry she can apply for an EEA family member visa. as the spouse of an EEA citizen exercising treaty rights in the uk.
I am assuming your gf has a current valid visa to be in the uk.