I don't remember this series, which surprises me. What were some of the classic trains in question?
It looked at more than just the trains themselves; it was part of a Channel Four franchise of "Classic ...." series', which also included "Classic Trucks" and "Classic Plant" (diggers and such, rather than foliage).
Having looked again, and found some more sources on the internet that mention the series, it's possible that there were only ever six episodes; strange, as it feels like more when they're all in order on one VHS tape. The episode list was as follows:
Season 1 Episode 6:
Loaded
John Peel explains how the post-war nationalisation of Britain's railways dramatically altered the role of freight trains
Opened with some shots from inside the abandoned hump control boxes at Toton, then looked at the operation of these hump yards in the fifties and sixties and then moved on to document the change from wagonload to trainload freight.
Season 1 Episode 5:
Express
John Peel examines how long-distance travel was revolutionised by express trains.
All about the "Big Four" and the "Race to the North" in the thirties. Lots of shots of A4s and Duchesses, including the video footage of the LMS 114mph speed record with "Coronation" that almost came acropper at Crewe, a bit about "Flying Scotsman" naturally, and the prototype Deltic also got a look in.
Season 1 Episode 4:
Shake, Rattle & Roll
Not just for train-spotters, find out how Britain's developing railways systems reflected social, economic and industrial development in the UK
Trams! Starting with a feature on the Isle of Mans' horse drawn trams (followed by the electric Manx Railway tramcars), and finishing with the then new devlopment of the Manchester Metrolink.
Season 1 Episode 3:
Slate & Narrow
John Peel examines the smallest and most eccentric steam train inventions.
Looked at the Welsh slate railways, and the Snowdon Mountain Railway. Also had a long feature on the Romney, Hythe and Dimchurch Railway, including footage of the "Laurel & Hardy" visit to the line.
Season 1 Episode 2:
Suburban Dreams
The century-long battle to provide an adequate train service between the city and the country.
An episode centred around third rail 'leccy land, the development of Metroland, and some stuff about the LTS lines before the 357s came along.
Season 1 Episode 1:
Coals From Newcastle
Early locomotives inspired by the need to shift coal in northeast England; an 18th-century railway unearthed in Newcastle.
The most part, if not all, of this episode was focused on North East England: There was some footage of the crumbling Stephenson Locomotive Works in Newcastle before it was refurbished, a long sequence at Beamish playing about on "Locomotion" with some chaldron wagons, followed by some of the history behind the rope-worked inclines. Also included a section on one of the early diesel locos, Armstrong & Whitworth No.2 at the Tanfield Railway, and also things to do with the continued development of industrial steam locos into the fifties which involved filming at the North Tyneside Railway Museum and on the NYMR.
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I saw this series when it aired and if I'm honest it's probably a significant source of my interest in the railways. As for what it covered, I recall programs that dealt with Welsh Mountain Railways, Tinsley Marshalling Yard (I think) and the end of rail bulk railfreight, another about Trams in Blackpool and an Island somewhere of the coast and there was one on the years prior to WW2 and others but I can't remember much about them.
I used to have it on VHS (taped from TV as I was out at Cubs when it was on TV
) but it's got lost and I would dearly love to have a copy on DVD (or even VHS if needs be).
Ditto; while at the tender age of seven/eight I was already "well into" trains, the Classic Trains series has to have been my greatest single source of railway general knowledge (It'll be my Mam who did the actual taping of it for me!). To this day I still think that it was a very tidily presented programme.
If I ever get time, I will probably copy my well played video taped from the telly onto a DVD-R at some point, assuming that its' still in a reasonable condition (It'll be at the back of a dark cupboard at my parents' house in Sunderland, which is no good when I'm located in Birmingham), but I would much prefer to get my hands on an official DVD release of the series if there is such a thing out there.
If you want a "blast from the past" then the whole series seems to be up on Youtube, albeit in short sections seven to ten minutes in length. Here's the first part of the "Express" episode:
http://www.youtube.com/watch?v=KAj0mOamChk&feature=related
Free beer! 
(Only been to one so far).