You only need to tell HMRC about living/working abroad if you expect to break your UK tax residence.
The key things to consider when working abroad is whether or not you complete a self-assessment return and whether or not you need to file a form P85. You should normally complete a self-assessment return if you are UK tax resident. This should be done in the year you work abroad and/or if you have any UK sourced income that will be taxable while you are overseas. If you work abroad, cease to be UK resident and you don’t expect to have any source of income which is taxable in the UK, you should consider completing a form P85 as you might receive a refund.