I used to work for Coutts a few years back (spent the first 5 or 6 years of my working life there). There is a difference between the requirements for an individual and a business.
Coutts offer business services and accounts like any other bank. I know that you are involved with patents and this is the sort of specialist area that Coutts might well be interested in. Traditionally they have strong links with insurance, shipping, legal firms etc. There aren't the same kinds of rules for company accounts as there are for personal accounts (when I was there, you had to have a minimum income of £100000 and assets of £500000 (excl property (this was about 5 years ago) for a personal account)
Coutts even offer student accounts - if they think you have potential!
Your best bet is to give them a ring and make an appointment with your local branch or go into one of the bigger offices - Strand or Lombard Street.
As the various replies suggest, there is no hard and fast way to open an account with Coutts - if the face fits and all that. If they think you have potential to earn big money, then they will take you on - it is as simple as that. If you are earning less than 40K a year and have a Coutts Bank account then the reason for this would normally be other assets - i.e investments, share portfolios, family trusts (or your family name ) etc
It is true that Coutts has traditionally been the bank of the armed forces and the royal family - which is where a lot of the snob appeal comes from.
I would have to say that having worked for them, the service provided is outstanding. They will run your (financial) life for you if you want - you name it, they can provide it. What people crave is personal attention. The staff to customer ratio at Coutts is around 1:300, at NatWest(now RBS), it is closer to 1:2500. Some Coutts account managers will look after as little 50 accounts, whereas your local high street branch, it is likely to be 10 times that figure. All this doesn't come cheap and there are plenty of people out there willing to pay for it, for whatever reason.
There are numerous private banks out there, some much more exclusive than Coutts (try C H ***** for example - you still have to be invited to hold an account with them). Coutts is merely the best known and one of the oldest (c 1692).
As I said before, company accounts are a little different and it would not hurt to have a chat with them as you might be pleasently surprised.
Not true, the reference to £3000 is the minimum balance you must keep in your current account to avoid bank charges (who does that ??). If it drops below that, you will be charged a fee for every debit and credit entry onto the account. It ain't cheap, so you got to want to do it. I would have to say that from the point-of-view of 99.9% of the people on this board there would be little benefit to banking with Coutts.
A little bit of trivia for you: It was my boss and I that actually secured the 'coutts.com' address, after a lot of wrangling
All I will say is that Coutts never washes it dirty linen in public! It guards it's reputation very closely and would rather settle it with the customer than slang it out in the High Court. Several other cases come to mind - Duchess of York, Sting being ripped off by his accountant a few years back. I guarantee that you do not know the half of it. There are ALWAYS two sides to every story.