In spite of the title, no action actually takes place on a ferry.
The locomotives that work the Night Ferry into Victoria in the morning and out again in the evening were designed to run on the "third rail" system of electrification. The first is a class 71 or a visually similar class 74. The loco that takes the train to Dover is a class 73. Classes 73 and 74 were electro-diesels, fitted with a small diesel engine for use in non-electrified yards and sidings. The train that Pyramid catches from Clapham (closely followed by Carol) is a 2-EPB unit, no. 5667. It was not scrapped at the end of its life but preserved and (in 2023) is awaiting restoration.
Many of the locations used are listed on the ReelStreets film locations website.
The route indicators on the front of the trains are as used by British Rail at the time (22: Victoria - London Bridge, 46: Victoria - Dover via Orpington, 75: Victoria - Dover via Chatham).
The "Night Ferry" service did indeed involve two separate trains. The main train was first class only and comprised the sleeping cars, baggage cars and restaurant cars. The second train, the one that Carol stows away on, followed the first. More of a budget operation, it only had seating accommodation. Its passengers had to make their own way from the platform to the ship while the sleeping passengers in the sleeping cars were shunted on board the ferry.