Some interesting comments here so far, but some also need further explanation.
Starting with the international movements, the proportional number of empty containers depends to a certain extent on the shipping line and the way the current market works which in general terms means there are between three to five times more laden containers arriving in the UK compared to number of laden containers exported.
The Asian shipping lines tend to attract greater support from their national countries due to the size of their domestic organisation and pricing policies whereas in the UK their organisation is usually very much smaller is largely geared to handling the import volumes. Unless a customer moves many containers, it's very unlikely they will ever see a sales person from the shipping line, to add to which most of this business is placed through forwarding agents or logistics companies who negotiate the pricing of the export movement with the shipping line. In contrast, the European shipping lines UK organisations tend to be based on attracting export cargo as traditionally this is the way they earned their commissions as a percentage of the freight against a much smaller fee for handling the import container. Today, most of the UK agents of the shipping lines are wholly owned subsidiaries of the parent shipping line so now they are treated as a cost centre so it's more a question of filling their allocation of laden containers on each ship which will be a set of multi-trade targets, whereas the Asian lines to a lesser extent will concentrate on selling space to a smaller number of customers who ship to markets where they need empty containers.
As a result, the European shipping lines may be loading from multiple UK ports, whereas the Asian Lines will tend to concentrate on one or two UK main ports. This also affected by the amount of feedering that the shipping lines operate, so for example MSC which is the largest shipping line in the world operates all it's own three main feeder services, to and from
1) Southampton, Portbury to from Antwerp/Le Havre
2) Liverpool, Greenock to/from Antwerp/Felixstowe, Le Havre and separately to Rotterdam.
3) Grangemouth, Teesport, Felixstowe and/or London Gateway to/from Antwerp
These are supplemented by additional vessels as necessary or by taking slots on their subsidiary WEC Line sailings.
CMA CGM operate their own feeder from Rotterdam/Dunkirk to Liverpool and Dublin and then tend to us BG Freight Lines which is wholly owned by Peel Ports for most of its feeder operation to all the ports served by MSC.
Maersk and Hapag has concentrated its Asian Europe/Indian Subcontinent trades on London Gateway, and it's Transatlantic trade on Southampton for the time being, but Maersk still uses exclusively BG Freight Line for it's UK and Irish feeder operations whilst Hapag follow a similar policy to a much more limited degree.
All the other global shipping lines also use BG Freight Line and DP World's Unifeeder, as and when necessary, supplemented by X-Press container line and one or two others.
Whilst Cosco and Evergreen both offer feedering opportunities the majority of their empty containers end up in Felixstowe and to a lesser extent Southampton and their import pricing for the UK inland delivery tends to reflect the round trip cost (port/delivery point/port) which is why during the Covid crisis the Port of Felixstowe, stopped accepting empty units back to the quay because they simply ran out of space and customers we told to return them to Immingham or Liverpool!
This sort of problem still happens from time to time at peak periods to other shipping lines as well, but they also have the advantage of switching volumes to other ports if the problem persists.
As far as Scotland is concerned, MSC is usually always looking for empty containers in Scotland followed by Hapag Lloyd, Maersk and CMA CGM because I suspect it's one area of the UK where export traffic is stronger than the import business largely because the import retail flows move via the retail outlets distribution centres in the UK.
Containers moving from Felixstowe, London Gateway and Southampton to Scotland will normally prebooked in advance of the vessel arrival, so if for example the vessel is delayed arriving or unloading is delayed by weather conditions, or port congestion on the Continent etc., can result in large number of late cancellations which can then result in the train loosing large numbers of containers if the spaces cannot be filled from other containers on the terminal which are available to move.
Turning to the UK domestic movements, i.e. Tesco etc, by and large I would not expect to see many empty spaces as these northbound trains originate from Tesco controlled distribution centres so they will maximise the space on a continuous basis from the stocks held in the distribution centre.
The southbound movements will contain the cages of returned or unsold stock and foodstuffs that cannot be disposed of locally etc, as well as cages of packaging etc that is to be recycled and of course the empty cages to be returned to the distribution warehouse.
The packaging will be collected then from the distribution warehouse by a specialist company who will sort it with other domestic recycling including newspapers and magazines, cardboard, and then it will be baled up ready for sale.
The plastic packaging along with off cuts from UPVC windows etc will also be baled or ground down to granules and bagged ready for sale. The recycling company or the party they sell these recycled material will then arrange to position a 40ft HC container at the premises where it will be loaded it to about 25 tonnes and check weighed ready for shipment usually back to China, Indonesia, South Korea or India for recycling.
These movements form important volumes for the shipping lines looking to return otherwise empty containers to these markets and move at rock bottom rates, often seemingly below cost and with the volumes from the rest of Europe, these volumes are the largest quantities moved eastbound.
This helps mitigate the cost of resituating otherwise huge volumes of empties and at the same time helps trim the ship as each laden 40ft then becomes equivalent to a 12.5 tonne 20ft which is a little under the optimum weight for a laden container when the lines calculate their planning and costings.
Outside the M25 the main areas for these recycling exports are the West Midlands, and the M62 corridor along with South Wales which conveniently means the volumes from the first two areas can be moved by rail, although the shipping lines may also use road transport if they are looking for a return load for import container tipping in the area.
And if you're wondering what happens to all this recycled material as well as recycled non-ferrous metals and electrical goods which move in the same direction to a lesser extent, it's simple.
Newspapers and magazines are de-inked and converted to pulp before being recycled into photocopy paper, whilst the plastic scrap is recycled into Xmas decorations and cheap plastic goods or components, whilst the card is recycled into new packaging to wrap the consumer goods etc we then purchase manufactured from the recycled metals and electrical goods which are then reshipped around the world.