London doesn’t really have a “centre” where all the attractions are neatly packed together. I post on TripAdvisor sometimes and there are often posts from tourists who assume London will be like smaller European cities where there’s a distinct downtown/centre area with everything in walking distance.

I recommend looking online at guides to London tourist attractions, deciding what you want to see, and making a rough plan.

My recommendation would be to go to the South Bank (take the tube to Embankment or Waterloo) - it’s a lovely area, the Houses of Parliament are right across the river, and you can catch a ferry or walk up to St Paul’s and then to Tower Bridge.

If you are prepared to drive into Kensington and find a car park I am a bit puzzled why the tube thing has you foxed! I do drive in London, but probably wouldn't choose to drive in Kensington and try to find a car park for the day, firstly because I don't know that area well enough to do back doubles and navigate one way systems and secondly because a days parking in Kensignton, if you find a car park, will be eyewateringly expensive. I assume there is a specific reason why you have to drive in, but if you can do as someone upthread suggested, find somewhere like
either of the Westfields use their car park and do the rest by tube. Make sure you use the same card to tap in and out and the days travel will be capped no matter how many stops and changes you make on the tube , bus or DLR.

Most of the seats on the riverbus are indoors, and even the outdoor section is undercover, so ideal in any weather. It’s really fun too!

You can walk to Buckingham Palace through Kensington Gdns and Hyde Park if the weather is good. Or get the 52 bus which goes onto Victoria Station where you can get the bus to Westminster Abbey/Big Ben/Parliament then a riverboat to The Tower. Or at Victoria Station you can go the other direction towards Waterloo for The London Eye. The riverboat is a great way to see the sights and you can get a hop on/off ticket. If you want to go shopping you can walk from Ken Gdns to Harrods and onto The Kings Road and Sloane Square.

How much time will you actually have, OP? I'm assuming your appointment is at an embassy, and in my experience, those can take absolutely forever.

And to be honest, what do you actually want to see or do during the time you have? Do you have a burning desire to go to the Tower of London, for instance? Because it sounds slightly as if you've randomly picked some tourist sights, the idea of getting around London by yourself is already stressing you out at the planning stage -- mightn't you be happier just hopping on one of the tourist buses and being ferried about that way?

The riverboat goes the length of the Thames so it all depends on where you want to go. You get on and off at lots of different stops. Maybe it would be easier for you if you tell us where you want to visit by importance, how much time you have, what time you will be arriving and whereabouts you are arriving. Ken Gdns is very large and have several entrances.

Agree with pp. Maybe a tour bus would be easier, you can buy ones with a river trip included. Just tell us what you really want to visit.

Download CityMapper, it’s excellent for journey planning.

Google maps give full instructions. I can’t manage in London without. It even tells you bus stop numbers.

maybe something like this but there are lots of companies doing the same and if you look at Groupon or Wowcher you might find better deals
www.theoriginaltour.com/en/tours/one-day-city-sampler-london-hop-on-hop-off-bus-tour

9 bus from anywhere along High St Kensington (probably the stop in front of the royal garden hotel). Get off at the Albert hall to see the museums, Knightsbridge for Harrods etc or Green Park for Buckingham Palace (and from there you can walk to Westminster and the South Bank).

I'm not sure of the tube/bus routes as not sure of your starting point, but if you get to Trafalgar Square, it is the nearest thing to the centre of London. (I know the number 9 bus goes there from Kensington High street or district/circle line tube to Embankment.)
From Trafalgar Square you can visit the National Gallery for free and it's a short walk along the Mall to Buckingham Palace. It is also a short walk in the other direction to Covent Garden. It's also a short walk to the Golden Jubilee Bridge across the Thames to the London Eye and South Bank.

I love the tourist buses, they stop at all the attractions and you can just get on and off when you like, plus the guides are usually nice

Use Citymapper and do some research. The Tower Of London is at Tower Hill - quite east from the London Eye and Buckingham Palace. You need to group the things you want to see - Trafalgar Square,St James Park, Buckingham Palace and then London Eye are all do-able starting from Charing Cross. Borough Market, Tate Modern and St Pauls all do-able starting from London Bridge - then you can go onto Tower Hill. But it depends how long you are in Lonfon - you might also want to walk along South bank from London Eye to the Tate/St Pauls. Or go to Covent Garden or Camden Market. Or get the Tate river taxi from Tate Modern to Tate Britain passing all the landmarks - much cheaper than the tourist services. Or even if you're here longer go to Kew Gardens!

Re Kew Gardens you now have to book a time slot in advance to gain entry.

River boat goes all along the river not across it! Though has stops on both sides I think.

@viques I'm also a bit puzzled by someone confident enough to drive into London but is a bit bamboozled by getting around.

The Woolwich Ferry does goes across the river rather than up and down it (and does a cool half-wheelie spinny thing in the process) but that's the only one that does. OP isn't likely to be anywhere near Woolwich. The ferry is cool though, and free, in case anyone's ever in the area!

Have you picked these things randomly or are they what you want to see?

God- please don't send the poor person to Kew Gardens if they've just got a few hours in central London. ( not that it isn't lovely...).
Am also confused about the driving bit- I live in London but have never and would never like to drive in the centre!I would also recommend WestfieldI you could practically walk there to KPG.
I would just get a red tourist bus OP and hop on and off when you like.
Tubes and buses are working normally and are noticeably quieter than normal due to lack of tourists.

Nearest tubes would be Victoria for BP, Waterloo / embankment for the eye and then Tower Hill. Unless you just want to see the outside you would need to pre book

In fact only 20 minute walk from Westfield to Kensington Park Gardens.
OP - where are you coming from?

OP isn't likely to be anywhere near Woolwich.

Well, no, unless the 'driving in London' thing goes a bit more than pear-shaped...

You do sound a bit clueless OP. Not a moral judgment, just a statement of fact which affects the advice we think appropriate to give you.

I agree you’re probably best off walking down to Harrods (Google or Citymapper apps will give you directions) and getting on an open topped tourist bus - if you’ve got time most of them come as a package with a tourist boat ride (and yes they go along the river not across it, some stops are on the north side and some on the south so you either pick a stop which is on the right side for you or you walk over a bridge).

I hope you have a lovely time. If all else fails ask someone. Londoners adore helping clueless tourists, it gives us a smug warm glow.