Looking for advice for broad 7-day trip

Need a little clarification what "big cities as possible throughout London" really means. Do you mean as many areas of London as you can or do you mean as many cities in the UK as you can? I am hoping you mean 1 week in London with a day trip or two out to surrounding areas.

I am unsure about your budget, but I would suggest looking into Premier Inns. They are not fancy or full of boutique features, but they do provide good value and offer quite a few different locations through London and the UK. In London, my favorite is Premier Inn Waterloo for location.

What types of sites or experiences interest you? Do you love history? Do you want to experience the pub scene? Would you like to visit tourist sites or more off the beaten path sites?

I believe they mean sites….

You may want to check out the RS London tour for ideas, they normally cover the main sites over a week.

When you say seven days are you including the arrival and departure dates into that seven? If so it really changes the dynamics. Also just curious why into Gatwick and out of Heathrow?

My apologies. I meant sites in London, not cities.

Westminster Abbey, Big Ben, Buckingham Palace, Windsor Palace, etc. are the big sites we mean to see. Trying to do everything we can, in our short visit. But I’m not really looking to help with that. Mostly just hotels because it’s just a vast area.

Modest budget, but I appreciate you taking that into account!
Love history, and local scenes.

9 days total, 7 days fully in london :)

Those airports because that’s what my husband picked lol. Honestly no reason other than it fit the flights we wanted. Didn’t care much about the airports.

7 days fully in London gives you a lot of time.

For a week's stay, I'd be tempted to look for an apartment or apart-hotel. London is a very expensive city, both to stay in and to eat in. Someplace with a kitchen will allow you to have breakfast and snacks in the room, at least, and save some time and money, if that's a consideration. Here is an example: https://www.tripadvisor.com/Hotel_Review-g186338-d3691506-Reviews-The_Rosebery_by_Supercity_Aparthotels-London_England.html

When we were in London the first time, we had a shorter stay, and we stayed here: http://www.tudorcourtpaddington.co.uk It is around the corner from Paddington station, where more than one tube line intersects, and the Heathrow airport train stops. Breakfast was included. The rooms were small, and the bathrooms smaller (be careful--not all rooms have a bathroom), but it was reasonably priced for London, very well-located, and the owners were nice. That was 12 years ago, so I don't speak from recent experience. (I was most recently in London last month, but only for a 20-hour layover, so I stayed in an airport hotel.)

Besides the sites on your list, I'd suggest Hyde Park (Peter Pan statue, Victoria and Albert statue, Kengsington Gardens/Palace, part of the Diana memorial walk), a play, the London Eye, and shopping in Carnaby Street.

One thing is that after you have determined your lodging choice, you should group your sightseeing together by proximity. One day go to the sites that you are interested in that are somewhat close to each other. For example, people often group Westminster Abbey (do sign up for the verger tour) with the Churchill War Rooms since they are located close to each other.

I like to do Tower of London first thing when it opens and then take a Thames cruise to Greenwich and explore there. The dock is right there at the Tower of London and it feels good to have some time sitting after wandering around the tower and all of the hundreds of stairs in the White Tower.

A moderate to lower budget is usually just the right match for a Premier Inn. Look at Premier Inn Waterloo or Premier Inn County Hall.

Parliament Square; Parliament, Elizabeth’s Tower with the Big Ben bell, Westminster Abbey.

Church War Rooms

Horse Guards

Buckingham Palace

Tower of London

Borough Market

Trafalgar Square

Greenwich

Camden Lock Market

Hampton Court Palace

Walk along the Regent Canal

Walk on the Thames Path

Have a pub lunch

Visit the numerous free museums

Visit the Crystal Park Dinosaurs

Check out the National Rail 2 for 1 deal

Theatre

EDIT Favorite Markets: Maltby,, Portobello Road, Brick Lane and Spitalfields.

ALSO, another vote for staying at a Premier Inn. The County Hall one is good, especially for first time visitors. Right next to Jubilee Gardens and the Thames. Easy 15 minute stroll across Westminster Bridge to Parliament Square..

We stayed in the Covent Garden/Soho area. It's a very lively area in the evening with plenty of restaurants. You're close to multiple Tube stations to get you anywhere you want to go and then at the end of the day when your feet are tired, you have plenty of restaurant selections close by.

Here's some advice from the host of this site: Rick's London planner

But a full guidebook will help you a lot, especially identifying things you don't know you don't know.

An area that we liked was the London Kensington area near the Gloucester Road tube station which was very convenient to take the tube to many sites. Another time we stayed near Paddington Station at Hotel Indigo.

Thank you all so much. Greatly appreciate the feedback :)

Another thought about any travel in Europe is timed reservations. Westminster Abbey, Cabinet War Rooms, possibly Tower of London, will require paid tickets. There are probably more, it’s a good idea to research to see those place important to you.

Just returned from 7 days in London, stayed in South Kensington near the South Kensington tube station. This is a lovely part of the city and easy to take the tube to all the major sites. I loved waking up early and exploring the surrounding neighborhoods. Be sure to explore the V & A museum and Hyde Park. For a day trip easily accessible via tube and overground train--Kew Botanical Gardens is fabulous. I would highly recommend this excursion out of the city to anyone staying for a week. Cheers!