Thanks for your question.
VAT MOSS is only relevant to Business to Consumer supplies of digital services. If the services are supplied business to business (B2B), then your supplies would be outside the scope of UK VAT, when supplied outside the UK.
Only your supplies in the UK would count toward the UK VAT threshold of £85,000, so you do not have to register for UK VAT unless you hit this threshold, but may wish to voluntary register. EC Sales Lists will be relevant only if you are UK VAT registered and making these types of B2B supplies.
As VAT is a self-assessing tax, please refer to the following links and follow this guidance.
Place of supply services (VAT notice 741A)
VAT notice 700/1: who should register for VAT?