Career path guidance Italy to London (or maybe not)

Hello everyone, I am a 2nd year International Economics and Finance (BIEF) at Bocconi University in Milan.

I need some help since I have so many doubts I don't even know where to begin with.

Like many students that want to break into IB, I realized it too late and I missed spring weeks and 1st year summer internships. Applying to London was a shitshow, and I realized that a good GPA was not enough to get interviews for London without any work experience.

So I started looking at smaller boutiques in Milan (BBs don't really take summer interns here) and I've found quite a few that seem interesting and I plan on getting in touch with. I didn't find much info online so if anyone has any experience or knows about these firms it would be extremely helpful. I am mainly looking at EQUITA, Cassiopea Partners, illimity, Vitale & Co and Mediobanca.

Now, assuming I manage to get a summer internship at any of these firms, I see three potential paths.

1- I finish my bachelors and I start working at the firm I interened at.

1.2 - I finish my bachelors, apply to BBs in Milan and I start working there. (I don't see a huge difference with 1 since I would still not go to London or do a masters. The only benefit I see from this is that a bigger name might give me a better shot for London (but I'm not sure so I'm asking you guys).

2- I end my bachelors and I apply to London. I manage to get an off-cycle (or full time) in London

3- I apply for a top masters program (LSE, HEC...) and go through the whole recruiting process in my 1st year -focusing exclusively on London.

I know this sounds very general, but my main questions here are:

- With my profile (Bocconi bachelors, summer internship at one of those boutiques or similar) is it possible to go for n.2 (getting an off-cycle or full time in London)?

- Does it make sense to start working at any of those after my bachelors to switch to London after some time? Is this doable? Would it be better if I go with 1.2, that is I apply to bigger BBs and after some time try to switch to London?

- Any comments on the banks I mentioned, if some are better than others, and if there are more I should look into.

Thank you for any help. There's very few discussions about such a career path here so I thought I'd ask and hope someone has any experience to share. Thank you so much!