London Eye, Big Ben, Houses of Parliament, Westminster Abbey, Parliament Square, Downing Street, Horseguards Parade, Trafalgar Square and Buckingham Palace
Whilst it is beautiful anytime of day or evening, check opening times and days for locations that you would like to visit along the route. The Changing of the Guards at Horseguards Parade is usually twice a day, once in the morning and once in the afternoon, so it is worth checking if you want to visit the parade.
Be vigilant in busy locations with your belongings as in any large city, and be extra careful of traffic when crossing roads. Remember that driving is on the left in the UK.