Can I recruit for Summer Analyst, having a full-time experience

Hi,

Looking out for an advice/opinion from people engaged in London SA recruiting.

Would a current full-time Investment Banking analyst be considered for Summer Analyst programs at London banks, or is this typically an automatic rejection?

For context: I'm currently completing an investment banking internship outside the UK, with a strong chance of receiving a full-time offer. However, I'm planning to pursue a master's program at renowned school in Europe and would like to recruit to London post-graduation. I am worried that not being considered for SA might diminish my chances to land a job at top banks. 

Should I start looking for new internship opportunities to still be eligible for SA, or potential conversion does not pose any hurdles for London recruitment post-graduation? 

Thanks for your help!