The Monopoly board game goes back to the 1900s and a UK version was created in the 1930s. There are 26 places and station on the board along with GO being named as Lambeth North tube station by Ordnance Survey during their assistance with the UK version. Places such as jail, electric company, water works and free parking are not explicitly named so I felt that it was best to leave them out for the sake of ambiguity.
The version of a FKT I decided on was starting at GO and visit all 26 places and station in the quickest time possible. I believe that the shortest route is as follows, but there are certainly many variations in the central area. The route I took was as follows; 1. Go (Lambeth North tube station) 2. Old Kent Road 3. Fenchurch Street Station 4. Whitechapel Road 5. Liverpool Street Station 6. Fleet Street 7. Strand 8. Bow Street 9. Leicester Square 10. Coventry Street 11. Trafalgar Square 12. Northumberland Avenue 13. Whitehall 14. Pall Mall 15. Piccadilly 16. Vine Street 17. Regents Street 18. Marlborough Street 19. Bond Street 20. Mayfair 21. Park Lane 22. Oxford Street 23. Marylebone Station 24. Euston Road 25. Kings Cross Station 26. Pentonville Road 27. The Angel, Islington. You also take in many other notable tourist sites such as Tower Bridge, Tower of London, St Paul's Cathedral and Buckingham Palace.
A useful resource was the following website, which details an alternative version visiting the above places in the order found on the board.