That's not really how regional distribution centres for supermarkets work. The inbound flows will come from a variety of origins; sometimes ports, sometimes the distribution centres of suppliers, sometimes direct from the manufacturers / food processors / farm producers. You'll rarely get more than around 3 artics into an RDC from the same origin in the same 12h period.
Let's start with everything except the ports. The origin points are rarely rail connected, and many will not send out more than a couple of lorry loads a day. The bigger ones will send out enough for a train load, perhaps 2, but they won't be going to the same destination - far from it. 50 lorries from a food factory in Yorkshire might go to 100 different RDCs of 5 or 6 different supermarkets. Just one artic full of, say, lettuces from Spain will come off the ferry at Portsmouth and be delivered to perhaps 2 or 3 RDCs. Rail can't do that.
There was / is(?) some limited traffic in refrigerated units that comes over from Spain by rail and through the tunnel; this was a bulk flow of produce from various farms to a concentration point in Spain that then took 24hrs or so to get to Barking. It was time critical, and door to door transit time was similar to road. If it was badly delayed (and it happened at least once) the whole stock goes in the bin. And then Chelmsford had no tomatoes the next day.
Ports traffic is a bit different. Any given port will see serval ships dock each day, unloading various numbers of boxes. Sometimes enough comes off one ship for one destination (ie container terminal), but more usually you need a few ships' worth. I think it would be quite rare for sufficient boxes to come off to form a train for one supermarket chain, let alone one RDC. However if the stuff isn't time sensitive (and it often is), it can go in the stack to wait for other boxes so that enough going to one destination can be made into a train load. Again, rarely would there be enough going to one RDC to justify a trainload. Hence the trains have boxes destined for several RDCs and go to the established intermodal terminals - eg Daventry, Trafford Park, Hams Hall etc, most of which have a number of RDCs - for different companies - in close proximity. The containers are then tripped by road to those nearby RDCs. The rail leg is thus a concentrated flow, over long distance, which is what works well for rail. Nevertheless for some products it works well. A large proportion of wine drunk in this country has been on a train at some point. Ditto electrical goods - fridges, freezers and power tools. Clothes, particularly at the cheaper end (the more expensive stuff is flown over). Toys. But there is rarely sufficent bulk to justify a trainload from one port to one RDC.
Of course there's exceptions to this at the margins - hence the Tescos trains up to and within Scotland - but the concentration & distance factors still apply. AIUI even then it's effectively a rolling road, the boxes to Inverness don't get unloaded at an RDC, they are usually off the train, on a wagon and then on the A9 to the destination store.
A new development is the principle of RDCs at the ports. Lidl have put a huge one next to London Gateway, and one of the other big supermarkets was going to also (not sure if they still are). The boxes come off the ship and are in the RDC in minutes. Potentially on a shelf in a store and then in your car boot within 24hours of being landed. No need to see a train at all.
