All of the immense system of railway tracks serving the docks in Dover was taken up donkeys years ago, Roger. It was all still in existence when I first arrived in Dover in 1987 and I have to pinch myself to believe that it has all gone without a trace, mostly concreted over for the road vehicles which have replaced the railway freight trucks. All the multiplicity of lines in the Western Docks have gone, including the sidings along Shakespeare Beach which used to house the continental freight wagons before the train ferry was rendered superfluous by the construction of the channel tunnel.
There are just the bare twin tracks of the mainline remaining. Therefore the only place where a steam train could halt in Dover for a couple of hours for a steam special would have to be in Dover Priory. One wrinkle that causes problems elsewhere but not in Dover is the lack of a turntable to turn a steam engine around. Fortunately, steam trains can come in from London on the original LCDR line via the Priory Tunnel and straight ahead back to London on the original SER line via the Harbour Tunnel. There were turntables at Dover Priory, the Marine Station throat, and the old Dover Town station sidings on the beach - later the site of the engine shed - but they all disappeared with the end of steam. It is still possible for a steam engine to run around its train in Dover Priory as there are crossovers at both ends of the Priory station. It could therefore go back the same way but with tender first running, which is frowned upon.
Interesting that the station manager states that the track is not a problem, just the watering, as I would have assumed it to be the other way around. All three platforms are in use for the Victoria, Charing Cross and High Speed to St.Pancras trains so I would have imagined that Southeastern would not look kindly on having one platform tied up for a couple of hours by a steam special. There are two sidings but these would also present problems. The train would have to come into a platform first for the passengers to alight. If it came in from the Folkestone end, then possibly it could pull forward and reverse into a siding should one be vacant. Not sure if it is permissible to reverse a mainline train in such a fashion even with the benefit of walkie talkies at either end. In steam days, a shunter would have pulled a train into a terminus platform whereupon the mainline engine would reverse onto the front of the train and take it away.
There would therefore seem to be two possible alternatives in making use of the sidings. Either the engine runs around the train and does its own shunting if that is allowed, or the steam special company goes to the expense of bringing in a shunter for the day. Either way, Southeastern might not entertain having the station tied up for the duration of these movements. Others may care to comment on this, Terry Nunn in particular is much more knowledgeable than I am on this stuff.
Digressing somewhat, the photo below is of Dover Priory back in 1876, with five locos in view. From left to right, this shows the goods shed, then the smoke blackened awning over the passenger platforms on the twin track mainline, then the long carriage shed, then the engine shed where the tall chimney is, then a loco on a spur which later became an Ordnance depot, then the elevated water tank on the far right of the photo with the water crane in front of the loco in the foreground. There were later further sidings on the left of the photo, where the carpark is today.
The water supply for the steam trains came from the elevated water tank which derived its contents from an adjacent well. It was later replaced by a taller structure on a steel frame. The well is still in existence and full details can be seen on Kent History Forum together with track diagrams (three pages).
http://www.kenthistoryforum.co.uk/index.php?topic=11193.0
Today, the steam specials pass through Dover and take water at Folkestone West where a water bowser is parked in the car park and hoses taken the short distance across the platform. The first few seconds of this You Tube video show the bowser.
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I watched Oliver Cromwell steam through Dover Priory some years ago and then raced over to Folkestone West and watched them taking on water. I would have thought that a water bowser could similarly be parked at the buffet end of Dover Priory station and hoses led directly across the platform in similar fashion. I suspect that the reason that they do not do this, and use Folkestone West in preference, is the difficulty of persuading Southeastern to release Platform 1 for the twenty minutes or so that this would take. However, this is purely guesswork and the station manager and the steam specials companies would be the people to ask.