I'm of the view that business and personal expenses should never be through the same account irrespective of how your business is set up (Limited Company, Sole Trader etc etc).
You should treat your business as a business from the very start or you'll ondoubtedly have further issues down the line.
Keeping them separate allows you to manage things much easier.
You can get into issues very easily with HMRC by running it all together to the extent that they could question certain expenditure and actually ask you to prove that you are running a legitimate business!
Imagine trying to do your tax return when it's all through the one account - doesn't bear thinking about
I think ultimately though it's about being professional and putting that across to your customers and with the range of free banking offers just now from pretty much all major high street banks it's not going to cost you anything to start out either