...the UK ? I have bad personal credit, however I will be starting a new company soon. Will this bad personal credit history affect my chances of getting say an initial overdraft for my company ?

It may well do .. there are many companies who are willing to lend to people with bad credit ..

If you go with them you pay a high apr

Bad personal credit record showed that you lacked fiscal prudence. You failed to managed your personal finances and you failed to repay your loan commitments as scheduled.

You must convince your lender that you do have the required ability to manage your finances and offer your explanation on the situations that led you to default on those loans. You must show documentary proof that those loans have since been fully settled.

Put up your biz plan and outline your biz strategy. State your level personal capital committed for this biz. State your expected working capital required [including your own capital] to get the biz started and operating. State the factors that will make your biz a viable biz. Your technical skills, your knowledge of the market, biz experience, your network of customers from previous employment. etc.

Convince them you have a competent biz partner with clean credit rating. Convince them that all decisions on the biz will be made jointly with your partner. Finance matters will be your partner's responsibility.

Most probably yes unless you have a very good collateral such as a property with enough equity or a guarantee by someone with good credit rating.

Overdraft are normally guaranteed by directors of those companies but as you say you have a bad credit history so your word is not worth the paper it is written on!.