Hi A!
First of all, congratulations on getting these offers and eventually deciding on Bocconi!
Thinking about Europe, I do suggest to look into the language requirements of different offices and evaluating your chances office by office. London is not the only office that only requires English. Besides, Amsterdam, Brussels and the Nordics are also offices that accept candidates without local language skills. Though this of course firm-specific and you should reach out to local recruiting teams to get the latest intel.
Regarding acceptance chances, you are right that London has a strong focus on Oxford & Cambridge. However, these are not requirements per se, so there is a realistic chance to get in, coming from other schools. The other EU offices typically work the same: While all offices typically have schools they are familiar with and can process applications easily, they will not reject you just because you are coming from Bocconi.
If you should apply to some of these firms, you would need to network to meet people from the respecive offices to understand as much as possible about the profiles they are looking for and the specific requirements they apply.
As most firms offer to have your application sent to multiple offices, there is no harm in having your application forwarded to UAE and European offices. Several of the candidates that I coached in the past were able to secure offers in regions outside their home country.