london: stay somewhere within 500m of gloucester road or south kensington stations
tube travel: buy your oyster cards before you depart: https://tfl.gov.uk/travel-information/visiting-london/visitor-oyster-card
many stations are less than a 5 minute walk from each other - plan your days on google maps before you leave home
https://content.tfl.gov.uk/walking-tube-map.pdf
changing tube lines at some stations wastes an incredible amount of time: green park, oxford, victoria.....
when you get off the train from manchester get in a cab and pay the sterling
westminster abbey: monday or tuesday morning at 0930 opening
you could spend a week in the british museum
the special hours for this year have yet to be posted for all of the top sites - for decades westminster was open wednesdays until 6 but that's not posted yet for '25
st. paul's is the other must-see in the religion category, unless you are in to masons, illuminati etc. then you have to go to the temple
if you must do the tower, combine with tate modern and again don't hesitate to pay for a cab - time is of the essence in central london
cabinet war rooms is a must - combine with westminster
national gallery, national portrait gallery, tate britain, tate modern, victoria & albert (take the elevator & start on the 6th floor), royal academy, are all must sees and there are 30 or 40 art museums after that group
personal favorites not on many lists: London Transport Museum, the Science Museum and Sir John Soane's Museum; the London Museum is moving and re-opening in the smithfield market in '26
you could do all of the above (but not the british museum) in 5 full days w/ a 6-night stay and that's with world-class planning & execution
& this is just scratching the surface