A lot of comments about Paris. So let's talk a bit about London.
I assume that you want to do regular sightseeing and take pictures of traditional tourists locations. Since you are not going for photography trip you will not be researching right time and right place to take picture of individual locations but just try to get best of what actually is in front of you (weather included).
First of all be prepared that London compared to Paris and Vienna has pretty messed up city architecture - there is literally no order and guidelines considering how a new building will fit into its surroundings. There is also nothing like real old/historic city center. Old and new is mixed up a lot and buildings can be very close to each other. Even famous landmarks are often squeezed among other buildings. Eg. St. Paul's Cathedral or Monument has really little space around. London is also a huge construction site with lot of cranes in the skyline and lot of lorries on roads.
You either like it or not. Either way there is a lot to see in London and if you are going only for a short trip you need to decide upfront what you really want to see and if it is enough to visit those places or if you for example want to take a tour inside. I live near London for almost 3 years, I work in City of London and there is still a huge list of places I even didn't visit once.
Some museums and galleries have free admission but places like Tower of London, St. Paul's Cathedral or Westminster Abbey are not the cheapest ones (you can't also take pictures inside Westminster Abbey and St. Paul's Cathedral) and it takes considerable amount of time to visit them. Transport in general is expensive as well. Depending on how long you are going to stay and what areas of London you plan to visit, there can be some cheaper options for transport.
If you don't mind walking a lot, I can recommend one walk we do with almost all friends when they visit us for the first time. The whole walk is about 9km but expect something like 12km. It is sightseeing walk which will still allow you taking pictures but since you are not going for photography trip you will not have ideal light for most of them. It will take you most of the day even without visiting any of the landmarks you will pass:
- Start in Green Park (tube station)
- Walk through Green Park to Buckingham palace - if you plan properly and visit in the morning you can see changing guards but be prepared for one of the most crowdy areas you can normally find in London (the worse is probably only underground in morning peak times). Dates for changing guards:
https://www.royalcollection.org.uk/visit/buckinghampalace/what-to-see-and-do/changing-the-guard
- Continue to The Mall and under Admiralty Arch to Trafalgar Square where you will see Nelson's column and National gallery
- Optionally you can go through St. James park instead of The Mall. There are few nice views of Buckingham palace and there should also be a local Pelicans "colony". You will leave the park at Horse Guards parade and you can get back to The Mall
- From Trafalgar Square continue to Whitehall. You will pass Downing Street and get to Parliament Square - by this time you saw probably the biggest squares you can find in central London
- Westminster abbey, Palace of Westminster (House of Parliament) and Elizabeth tower (Big Ben) are all nicely visible from Parliament Square and you can take some nice pictures even without UWA lens
- From Parliament Square cross the river over Westminster bridge. Again nice view of Palace of Westminster and Big Ben and also London Eye. Palace of Westminster is currently ongoing partial renovation so don't expect to make postcard style picture
- Once you get to the south bank just turn left to London Eye and continue till you get to Tower bridge (about 6km)
- During this walk you will see many other landmarks and points of interests including:
- London eye
- Southbank Skate park
- Oxo Tower (I've never been there but there should be a public viewing platform next to the restaurant)
- London Blackfriars (Bridge which is a Train station)
- Skyscrapers in City of London (Gherkin, Walkie Talkie, Cheese Greater)
- Distant view of St. Paul's Cathedral
- Shakespeare Globe
- Tate Modern
- Millennium Bridge - If you feel tired here you can just cross the bridge and walk towards St. Paul's cathedral where you will find a tube station. You can do rest of the walk another day. If you continue another day I would recommend adding Borough Market as well - it is on London Bridge close to Shard.
- Golden Hinde II
- Shard
- HMS Belfast
- Tower of London
- City hall and More London
- Tower Bridge - if you are lucky you can see bridge lift. Check
http://www.towerbridge.org.uk/lift-times/ for planned lifts
If you don't cross Tower bridge and continue a bit you can also see interesting Shad Thames street. Otherwise you can just cross the bridge and end your walk in Tower Hill tube station.
It is nice both during the day and in the evening/night and since you will be taking a lot of pictures over the water 24-70 zoom range will be good and you will also find use of 70-200.
If you don't like walking so much, interesting option can be using Hop on Hop off bus (I think there is multiple providers, just search on Google) because that will take you around all important landmarks.
Apart from the mentioned walk another popular places for tourists include:
- Getting closer to St. Paul's cathedral
- Oxford street and Oxford circus (it is mostly about shopping)
- Piccadilly circus (I found it extremely boring but people usually want to visit it)
- China town (close to Oxford street and Piccadilly circus)
- Hyde park, Marble Arch, Wellington Arch, Kensington gardens and palace
- Harrods (department store in impressive building)
- Natural history museum - another impressive building
- The British museum
- Covent Garden
- Portobello Market in Notting Hill
- Madame Tussauds
- Greenwich
Be ready to have option for both good and bad weather or take an umbrella and camera rain cover. Spring and summer in London are not too rainy but just in case ...
My walk around set for London usually does not include 24-70 zoom. I always take 16-35 and usually 70-300 and tripod.