Since our only income is from property rental it was never worth our while even to consider pursuing non-domicilary status, since even non-doms pay UK tax on UK rentals. In any case, a vagabonding lifestyle makes it very difficult to qualify as a non-dom since it’s not possible to show that you “reside” anywhere else, and our life would be very difficult, probably impossible, without a postal address in the UK – and HMRC would seize on that as proof that we are “ordinarily resident” in the UK.
Depending on the complexity of your affairs you might want to engage an accountant, but in simple situations submitting your return online should work fine. We already had an online account with HMRC set up – it takes up to 3 weeks and involved a letter, so can’t be a last minute thing. We set up direct debits to cover some tax payments that were due while we were away, and can make payments while travelling if necessary
The one bit of non-dom paperwork that we had to complete was an NRL1 form. If you are not in the UK and are using a letting agent to rent property, the agent has to collect tax on the rental unless you get prior approval from HMRC to receive the rent gross and then pay the tax yourself. Since our income would barely reach the tax threshold, we certainly didn’t want the tax office taking a too-large cut up front.