It's not quite that simple. Even the ships carrying the least sensitive cargoes will normally have at least a Reservist onboard as liaison and to "keep an eye". Those carrying items more vital such as sensitive equipment or ammunition will normally be RFAs or Strategic Sealift vessels which will carry a full crew of reservists. As well as RN planning, the RN also monitors such ships via satellite and other communications methods via Northwood and the likes of UKMCC in Bahrain, with local RN units kept informed should they be required for escort or assistance purposes.
One of the lessons learnt as far back as the Falklands was that there simply was not sufficient suitable tonnage available to the MOD, even at that time when the UK had a large fleet (in comparison with today). By suitable I mean British flag, built to appropriate construction standards for a war zone, able to carry the kind of cargoes required by the modern MOD (Ro-Ro, containers and break bulk), able to work with aircraft in a limited fashion, have specific comms gear onboard and also able to interface with Mexeflote and landing craft.
The 1998 defence review actually addressed some of those lessons from 1982 and 1991 and resulted in the procurement of six such suitable ships of which it was only envisioned three would be required at any one time, the other three could operate commercially and generate revenue for the MOD or at least cover operating costs. In reality 4 were needed full time and occasionally a 5th. Roll forward to 2012 and the new government got rid of 2 ships, stating that if more are required they can be brought in on private charters. Literally 2 months later they then chartered in two ships at roughly 3 times the cost of the "in house" vessels to try and cope with the backlog of kit to be brought home as the result of the drawdown from HERRICK (Afghanistan) - clever eh?! Yes, even British operations in Afghanistan (a land locked country) depended on resupply by sea, usually from the UK to ports in Cyprus/UAE/Pakistan where it was then flown directly in on a short hop basis or in the latter case driven up country.
One of the ships I've mentioned is that seen above (a ferry?!) and is indeed fully crewed by RN sponsored reservists and operated/tasked by what was known as DTMA then DES and is now something partly privatised, but basically an MOD tri-service logistics organisation.
Now, there's little point in having these vessels or any others as part of a supply line or amphibious task group if there's nothing available to protect them and nobody able to organise it all - which is where the RN comes in.