Escalator etiquette is very stern in London. The main place you will probably encounter escalators is in the tube stations. The custom is to stand on the right side...DO NOT stand in the middle of the stair. Stand to the right so that if someone wants to walk up the escalator steps, and a lot of people do, they can pass you on the left. People will get testy if you are blocking their way.
Everyone knows that the driving is done on the opposite side of the road to what most of the world is used to. Many intersections where there are pedestrian crossings have warnings painted on the road to make you remember which way to look. There are also light change signals with green men that signal it's ok to walk. But the locals will often go anyway if the traffic is clear. Me, I will only go on the lights or if there's a crowd going, I'll go with them. If I'm going to die, at least I'll have company!) Then there's the famous "Mind the Gap" warning in the underground. The trains don't come right up close to the platform quite often so there may be a bit of a space to walk over. Just watch where you're going.
London lights up for the Christmas season. Oxford Street, Bond Street, Regent Street, Carnaby Street and in between, there are beautiful window displays, lights and decorations wherever you look in the shopping districts. Walk and look but watch the traffic. Best places for pictures are the traffic islands as you cross the road.
London is fairly flat so you won't likely have too many hills to climb unless you're out in Hampstead or Greenwich. Take a collapsable umbrella because you never know when it's going to shower!
Souvenir shops and stalls are everywhere in the city centre but if you want cheaper souvenirs, go up by Bayswater Road and Queensway for excellent prices on tat and postcards. Far cheaper than Covent Garden, Oxford Street and Leicester Square.
The attractions, restaurants and shops around Piccadilly Circus and Leicester square are VERY expensive. It's worth seeing it lit up at night, mind you but for eating or shopping, go elsewhere. Oxford Street might be a shoppers' haven but most of the stores aren't particularly cheap there either though you do get a good variety. Marks and Spencers is always worth a browse and, while posh and expensive, Selfriges is nice to look in as well. Harrod's, for me, is a bit of a tourist trap. The food halls are worth seeing but mainly the store is overwhelmingly large and very over priced. I'd go to Fortnum and Mason on Piccadilly instead. It's not cheap either but you won't get lost and they have a good food hall as well. Hatchard's, an old bookstore, is next to F&M and is a lovely shop! Dark walls, lots of stacks and shelves, a spiral staircase and a fantastic selection. The best area for books is on Charing Cross Road where new bookstores and second hand ones line several blocks. Also on Tottenham Court Road (which is the other end of Charing Cross Road north of the TCR tube station) are a lot of electronics and music shops.
Some museums, galleries, cathedrals and other attractions may be open one evening a week until about 8 o'clock or so. They will often have reduced entrance fees for that so it's worth checking out.
Picnics in one of London's great parks or leafy squares are always a nice respite from all that walking. Hyde Park and Regent's Park are the largest, each with ponds, boating lakes, bandstands and gardens to look at as well. You can also bring alcohol to your picnic and drink it there and nobody will object (unless you get drunk and obnoxious, obviously) Hyde Park has Speaker's Corner on Sunday mornings where people get to stand up and rant about their particular bees in their bonnets.
There are a lot of things I haven't mentioned, and everyone finds their own London. Places I haven't been to but would like to some day include the Dulwich Picture Gallery, Notting Hill and the Portobello Road market, Petticoat Lane market, Borough Market, George Inn (Southwark, an old coaching inn), Tea and Coffee museum, Guildhall and clock musuem. Places I've been that I want to see again include the National Gallery, Museum of London, British Library, Hampton Court, Globe Theatre museum, Tower of London and maybe Greenwich. My favourite thing to do in London is just to walk and wander off the main roads into the side streets to see what's there, the little squares, the old buildings. I generally stay in the city centre so i'm not in any of the more notorious parts of London and you can't get that far lost.