Regulation for rewring back box?

I want check do I need part P certificate, or planning permission? 

Generally no - simply replacing an existing back box would not normally be notifiable under building regulations (and nothing to do with planning either).

The details vary depending on which nation you're in (Wales has building regs that tend to lag England's a bit and Scotland and NI have different approaches again) - the English ones for example can be found here: https://www.gov.uk/government/publications/electrical-safety-approved-document-p

Where work is notifiable under part P of the building regulations, there are a number of possible routes: Generally either pre-notifiy to your local building control dept (which costs a significant amount of money) and they'll make sure it's OK and issue a building control certificate (which is basically the method builders traditionally use for foundations and drains and the like and can also be used by DIYers); or you get a member of a registered competent persons scheme to do the work (they can then self-certify the work) - note that it's the membership of a scheme that counts rather than holding any particular certificates.  In theory there's also a third-party-verifier scheme where a registered competent person with an add-on to their registration can oversee the work (e.g. done by a DIYer) and issue a building regs certificate but they seem to be rather thin on the ground.

In any event you should be competent to do the work you undertake - whether it's notifiable or not. Competent isn't the same as qualified of course - a decent DIYer working well within their limitations could well be competent to carry out straight-forward electrical tasks without needing any electrical qualifications for instance.

If the property is privately rented there's no also a legal obligation to ensure that the electrical installation complies with the 18th Ed of the wiring regs - and in such cases if you were the tenant you'd perhaps need the landlord's permission too.

  - Andy.

I want check do I need part P certificate, or planning permission? 

Generally no - simply replacing an existing back box would not normally be notifiable under building regulations (and nothing to do with planning either).

The details vary depending on which nation you're in (Wales has building regs that tend to lag England's a bit and Scotland and NI have different approaches again) - the English ones for example can be found here: https://www.gov.uk/government/publications/electrical-safety-approved-document-p

Where work is notifiable under part P of the building regulations, there are a number of possible routes: Generally either pre-notifiy to your local building control dept (which costs a significant amount of money) and they'll make sure it's OK and issue a building control certificate (which is basically the method builders traditionally use for foundations and drains and the like and can also be used by DIYers); or you get a member of a registered competent persons scheme to do the work (they can then self-certify the work) - note that it's the membership of a scheme that counts rather than holding any particular certificates.  In theory there's also a third-party-verifier scheme where a registered competent person with an add-on to their registration can oversee the work (e.g. done by a DIYer) and issue a building regs certificate but they seem to be rather thin on the ground.

In any event you should be competent to do the work you undertake - whether it's notifiable or not. Competent isn't the same as qualified of course - a decent DIYer working well within their limitations could well be competent to carry out straight-forward electrical tasks without needing any electrical qualifications for instance.

If the property is privately rented there's no also a legal obligation to ensure that the electrical installation complies with the 18th Ed of the wiring regs - and in such cases if you were the tenant you'd perhaps need the landlord's permission too.

  - Andy.