I've just accepted employment elsewhere, what do I need to do?

This depends on whether you are currently receiving a salary from your own company.

Already paying a salary:  unless you want to be paid at basic rate of tax (e.g. tax being deducted on the full pay at 20%) then it is advisable to stop paying your wage from the company. There is no tax benefit in keeping both wages active and you will pay more tax during the year. 

In order to ensure your remaining personal allowance is transferred to your employment, your employment with your limited company should be stopped and a P45 provided to your new employee. It should be stated that you do not have any other jobs. 

Not paying a salary:  there is nothing you should need to do, but ensure you are being taxed at the correct rate from your new employer.

You should also review the level of dividend payments you receive during the year.  If your new salary is much higher than the wages declared through the company then the dividends paid may be subject to a higher rate of tax.

Always notify your accountant as soon as your circumstances change, and consult your accountant as to how best to handle your new earnings structure to ensure tax efficiency over the year.