If you're in business as a sole trader (self-employed) and you don't have a Personal Tax Account (and who does?!) you can only tell HMRC of your change of address by writing to them or phoning them.
I don't recommend writing because it will take HMRC weeks to deal with your letter.
Call the Income Tax Helpline on 0300 200 3300. You'll need your National Insurance number and ideally your ten figure UTR (Unique Tax Reference).
You'll probably be asked for your date of birth and your last address (the one HMRC are using).
When you've given them the details of your new address make sure you ask them how long it will take for your records to be updated.
P.S. If you do decide to write use the address on the most recent correspondence you have from HMRC.