Graduate FT Offer and Visa Issue

First time posting on here, excuse me for any mistakes. 

I am based in the UK and am currently in my final year at university at a target university. I've interned and received a FT offer from a top BB bank in Private Bank (think HSBC//JP/UBS etc). I currently am here on a visa. However, due to the new rules of immigration & government (thresholds, costs), the bank has alerted me that as of now, after the graduate scheme I will not be able to be sponsored by the bank to stay within the country. 

My conundrum is, after accepting the offer, what is the best steps that I could take (apart from doing a well enough job on the grad scheme to somehow convince them to sponsor me) to ensure I could end up at a place that would sponsor me? The risk is too high as if I don't get sponsored after the 2 years, I am at risk of leaving the country if no other bank picks me up + I can't lateral anywhere within the Bank that does sponsor (however, this is a big unknown as have no idea of the availability of those divisions in 2 years time)

Would love any piece of advice that you could share. I am still applying to other graduate schemes but due to me needing sponsorship, a lot of shops are giving me auto-ding. I also have a year in industry under my belt in Markets as well so my CV isn't the issue.