From a Non-Target but I have a very solid CV. SA 2023 LDN possible ?

As the title indicates, i'm from a semi-target in the UK, and I will be applying to summer analyst roles for 2023. If you have spent enough time on this forum, you'll know that breaking into banking as a non-target is not the easiest of tasks. But on the bright side, I have been able to develop quite a strong CV over the past year. it ressembles someth like this:

Work experience: 

Summer intern at top 4 pb worldwide (GS/BNP/CS/UBS)

Spring intern at very good AM in UK 

Leadership pos at student firm 

Trilingual etc etc 

Realistically speaking, how much better are the odds of someone from Oxbridge/ LSE/ UCL/ Warwick getting a top SA at BB/EB compared to mine given all of these factors ?

Thank you