Travel from Heathrow to your hotel in St. James; fastest public option is Piccadilly Line to Green Park (then 8–10 min walk) or Heathrow Express to Paddington + taxi; pick the option that fits your luggage/time. This places you in the heart of central London for walking to major free sights.
Stroll through St. James's Park to the outside of Buckingham Palace; the park is beautiful in autumn and the palace façade is a classic photo stop — free and open most daylight hours.
Walk past Horse Guards, down Whitehall to Westminster; photograph Big Ben and the Houses of Parliament from the riverside. These are exterior viewpoints and free any time (check scaffolding/works online).
Dine conveniently at The Game Bird (in the Taj property) for contemporary British dishes, or try nearby Classical British at Fortnum & Mason Grill if you prefer; excellent to avoid more travel on your arrival day.
Watch the Changing of the Guard or visit Horse Guards Parade — viewing is free but the Guard schedule varies so check the official site the night before.
Visit the National Gallery to see masterpieces by Van Gogh, Turner and others; entry to the permanent collection is free and the building is central and easy to reach (usually 10:00–18:00, late openings some days).
Walk to Covent Garden for a lively lunch at Dishoom (Bombay-inspired menu) and enjoy the market and street performers nearby — book if you can as it’s popular.
Head to the British Museum to see the Rosetta Stone, Parthenon marbles and world antiquities — permanent galleries are free (typical opening ~10:00–17:00).
Freshen up at the hotel. If you fancy theatre, book a West End show for the evening — good choices include long-running musicals and plays (tickets from GBP35+).
For dinner try The Cinnamon Club (modern Indian in a grand setting near Westminster) or Rules in Covent Garden for historic British dining — both are classic London restaurants and should be reserved.
Have an early breakfast at the hotel for convenience (or try a local café such as Gail's or The Wolseley) — you'll want to start early to fit a few more free sights before leaving for Reading.
Start at Tate Modern (permanent collection free) and then walk the Southbank — this stretch has great riverside views, street performers and free galleries/spaces; Tate usually opens 10:00.
Walk to Borough Market for a wide range of food stalls offering everything from British cheese to international street food — market hours are generally morning–late afternoon (many stalls open by 10:00).
Cross over to the north bank to view St Paul's Cathedral from outside — interior visits are ticketed, but exterior photos and the surrounding area are free.
Enjoy an early meal near your hotel (The Ivy St. James is conveniently close) so you can collect luggage and head to Paddington for your train to Reading.
GWR fast trains run frequently to Reading (approx 25–30 minutes); book in advance for best fares. Aim for a train around 19:00–19:30 if you planned an evening arrival in Reading.
Reading is a good base for short day trips: Windsor Castle (paid), Oxford city centre (train ~30–60 min) or Henley-on-Thames riverside. Pick one depending on your interests.
If you go to Windsor, see the Castle (note entry is paid and timed) or head to Oxford to walk the colleges and libraries (many colleges free to view from outside).
Early breakfast and prepare for another optional day trip — Bath & Stonehenge tours operate from Reading/nearby stations but require full-day planning.
Check out and take an early train from Reading to Paddington (fast trains ~25–30 min). Arrive at Paddington and taxi or Tube to the Taj in St. James to drop luggage and refresh.
If you still have energy choose one free museum (Natural History or V&A — usually 10:00–17:30) or head to Harrods and a Hyde Park walk for relaxed shopping and photo ops. Pick one to avoid rushing.
Leave the Taj by 17:00 for Heathrow (taxi or pre-booked car recommended). For an 20:00 international flight, arriving 3 hours early is sensible; allow extra time for traffic and security.