Summary: What is the simplest way for a UK business to obtain a USD
bank account with a debit card (probably Visa) attatched to it?

We are a UK business and we wish to open a USD bank account that has a
debit card attatched for us to pay our US-based suppliers with (paying
from a GBP account is getting expensive since our bank takes 3-4% on
the currency conversion).

Our current bank offers USD accounts, but only for cheque payments -
there is no card attatched which is useless for paying our US
suppliers. UK banks only seem to offer cards with personal accounts,
and US banks dont generally offer accounts to overseas businesses.
PayPal only issue their virtual debit cards for US
businesses/residents too.

I have seen some sites that offer exactly what we need (eg.
http://www.usbankaccount.com/) but a) its rather expensive and b) I'm
not in the habit of sending large sums of money to people I have never
heard of! I would prefer a solution I can manage myself, or that deals
with known entities (such as a major bank).

I think my ideal answer would be a referral to a UK bank that offers
what we need but that I have for some reason not found.

I was recently in London and found that Barclays Bank of the UK
http://www.barclays.co.uk/ is affiliated with BANK OF AMERICA US
http://www.bankofamerica.com/.  I don't know the answer to your
specific question, however I was able to bank with Barclays during my
stay as if I was at home.  Hope this helps.