There are lots of institutions within HMRC. Here are full guides into how to complete your address change with all of them.
The full guide on how to update your address with HMRC online within minutes
When moving home you need to tell Child Benefits that you've changed address
The Department for Work & Pensions needs to be informed when you move
If you're changing address, the administrators of your Personal Independence Plan (PIP) need to know
Complete your address change for your Employment Support Allowance (ESA)