British citizen coming to work in Montenegro

In that case you will need working permit for cross-border services.
First of all, that company you are working for needs to have some kind of agreement with company from Montenegro.
Second is copy of registration of Montenegrin company.
Copy of passport (just first page)
Proof that you are actually working in that company (foreign)
Copy of proof that you are registered for health and pension insurance in country of your origin.
Receipt for payment of 10e on account of "ZZZCG" 832-3200-06

With all this you will get working permit, and then you can apply for visa, and for that you will additionally need:
Registration of tourist stay for 30 days - 21e
Proof that you have enough funds to live (the easiest way is to open account in Montenegrin bank and to deposit 300e, and to get proof from them that you have 300e on the account, later on you can pick up that money)
Proof for health insurance which can be used in Montenegro (if you have it in your country and country has deal with Montenegro about this) or to pay travel-health insurance in company in MNE - 25e
Copy of all pages in passport.
Stamped copy of first page (in Court, or Municipality or at Notary)
Translation of first page.
Proof that you have accommodation here.
Payment of two taxes of 5e and 10e on account of "MUP CG" 825-50-71

To be honest it can be complicated for you if you do not speak language. Agencies ask 100e for this and you have 115e of expenses.