mistake

Username checks out. From my understanding FT recruiting has been EXTREMELY difficult this year and some of the banks you mention have not even taken in FT recruits. If any of the banks mentioned even hire full-times, the recruitment is likely to be finished by now. The difference between Citi/BoA and GS/MS/JPM isn't nearly as big as you think. Citi and BoA are both extremely strong in Europe and you will work on very similar deals as you would in GS/MS/JPM. Obviously, GS/MS is a better brand name and you might have marginally better exit opportunities. Meanwhile, you will get interviews at most places from Citi/BoA as well. Moreover, you will get absolutely crushed at GS/MS. I will stick my neck out and say that MS probably has the worst culture in London. It is extremely well known to have rough hours and a shitty culture. Everyone I know who has been there absolutely hated it. From my understanding, the culture isn't as bad at GS but the hours are extremely rough and I know several people that have just quit without having another job. 

With that said, your opportunities of getting a full-time position in this market environment and this late in the recruitment cycle are extremely small / non-existent. Even if you did get a FT position, the benefit would be marginal and hours / culture is likely to be significantly worse.