The game was played on a board displaying the central section of the Underground map, each player controlling a counter, moved around the board at the roll of a dice. Before play commenced, around six cards from a set naming Underground stations on the board (and giving details of places of interest nearby, in keeping with the overall theme of a tourist's visit to London) were dealt out to each player. The object of the game was then to begin (from their "home station", which had to be a BR interchange, again maintaing the "tourist" theme), visit each of the stations listed on their cards, and return to their home station, the winner being the first player to do so.
The major barrier to achieving this goal was that whenever a player changed lines, they had to take a "Change" card (remarkably similar in both name and format to "Chance" cards in Monopoly), which would be either beneficial (eg, roll again) or detrimental (eg, forced to go to Paddington to pick up lost property). Whilst a somewhat diverting entertainment, this game had none of the subtlety and depth of MC itself, and recent research in Hamley's shows that it does not appear to still be generally available.
This sounds very much like [The London Game], which should still be available from the London Transport Museum (in either full or magnetic-travel size). It makes a reasonable replacement for a proper Crescent board, if you can't afford the full Corner & Side mahogany set - you lose a lot of the outlying stations, and don't get many tokens (although there are some nice Block ones), but it's good for a quick game.