When you have another offer on the table the best move for the recruiter is to make the serious offer then and there and try take care of the situation to avoid any further bidding.
They want you for as cheap as they can get you but if someone else is willing to pay more then almost always they can afford it.
You are comparing a bank to a startup which is an absurd comparison. Compare Goldman to Google and guess what Google wins (even in London).
Banking salaries have been static for 10+ years. Bank internship salaries are designed to allure and impress but 5+ years in and the salary does not change.
On another note there are some startups who can pay very very well in London but they do not advertise these salaries.
Only if you are a Trader or an Investment Banker (note not the other 98% of people working at the firm i.e. Tech, Quant, Operations, Finance, HR) in which case you are already the handful of people such as the ultra high paid at Google as either your career is going to be very short once they find out you can't make money or you are very good (very few people) and you will make a fortune.
As a current Goldman Strat I can confirm that the hoodie-wearer is certainly out earning the majority. Only the traders are paid well, everyone else is on a less than competitive wage based on an illusion of how it "used to be". Historically (10+ years ago) the total compensation was accounted for by a big bonus but these days it is non existent.
Almost every VP I know in NYC/LDN makes less than a fresh grad at Google in the bay area.
They want you for as cheap as they can get you but if someone else is willing to pay more then almost always they can afford it.