Consider the following:

• Please make sure that it is a registered accountancy firm
• Find who is it registered with like ACCA, ICAEW, CIMA etc. It is important in case if there is any misconduct so you can report it to the relevant authority.
• Ask an engagement letter or contract
• Keep the key correspondence through email rather than verbal
• Check how opened is i.e what others are saying about the firm. You can check it on Google Review, Trustpilot etc.
• Make sure that you talk to a few accountants before so at least you would know what you should be expecting from the accountant as well as the cost.
• Remember, ask for the full accountancy fee, which you can pay every month through a direct debit.