nomis5 - 10:37 pm on Jan 20, 2013 (gmt 0)
Back to the OP, IanCP's advice is good but be clear about the exact circumstances.
1. Both accounts in the name of John Smith
2. One account ino John Smith and one in joint names of John Smith and Jim Joness
3. One account ino John Smith and one in name of a limited liability company of which John Smith is a director?
Imprecise use of terminology (eg calling something not an LLC a "company") could lead to you loosing an account because G understood it to be something different to what you were doing.
The above may be an over complication of something which is relatively simple.
If the reality is that you have a functional business with an account in that name and a personal account in another name and they are truly two different entities then you will be OK. The minute you start mixing joint accounts into the mix then you might well be in trouble and if you get caught you deserve it. Keep it simple and true.
Personal and business accounts are OK.