I'm afraid that the HMRC definition of complex estates effectively includes any estate which establishes a will trust if the will trust incurs a UK tax liability (e.g. income/capital gains/SDRT/SDLT) during the relevant tax year. It also includes any other express trust. It is all contained in the draft Money Laundering Regulations 2017, which are likely to come into force in July/August.
(the formal term is "relevant taxable trust").
I would expect a NRB Trust holding investments to be caught. The online portal does not yet exist, in part because the election has delayed the regulations.
The obligation is to register by the end of the tax year (ie by 5/4/18) and then update or confirm each year there are tax liabilities.
Note that the regulations also require significant record keeping by the trustees (who need not be professionals) - see Reg 43 here:
https://www.gov.uk/government/uploads/s ... _FINAL.pdf