March is actually the driest month of the year in London. There aren’t that many more rainy days than there are in San Antonio at that time of year (11 days per month vs. 7 days). However, I imagine it is more prone to those protracted periods of on/off drizzle, whereas Texas rain is probably more dramatic.
http://www.bbc.co.uk/weather/world/city_guides/results.shtml?tt=TT003790
The OP’s wife & daughter are taking the trip. If they follow the ultra-casual suggestions here, they can pretend they are Rose & Jackie Tyler! (Before they moved to Pete’s World & were able to afford better clothes.)
Most people I know wear jeans, but not with white sneakers.
I am wearing jeans and trainers right now. And I am at work. In London.
(OK, so I work in a place with no dress code, which is great as I tend to dress for work based on what is nearby in the morning and doesn’t smell* but most of my colleagues dress in a similar fashion).
Echoing a bit of what others have said, I think jeans and trainers is fine day to day. Even the style doesn’t matter that much. It’s thought of as very casual, so if she was heading off somewhere elegant she’d be better off with smart shoes and trousers/skirt. I don’t know what the Orangery is, evidently I am an ignoramus.
Tourists stand out in London for reasons other than fashion, here are some reasons:
*Some days I relax the rules regarding smell, these tend to be Mondays when I leave it to last minute to get out of bed.
I live in London and I do, in fact, wear a cowboy hat. It’s sitting on my (work) desk right now, next to the computer. It keeps the rain off my glasses during the commute. And I’ve seen a small number of other (male) commuters doing the same, including one fellow on my train who wears a full duster as well. They’re practical hats, as long as you’re not wearing one of those goofy ten-gallon ones.
I occasionally get comments, but mostly from drunk people.
When I was there two years ago this March, it rained or drizzled two out of the four days I was in town.
What if they bump into the Queen at a bus stop or some such? Better to dress a little nicer just in case.
What? You think that the Royal Coach is the kind of coach that stops at bus stops to pick up passengers?
They won’t stand out in jeans and trainers. They will stand out in sandals or flip-flops. Especially in December.
Unless you are a member of Run DMC and it’s 1985, most people here in the US don’t wear that either.
When I visited London about a year or so ago, people pretty much seemed to wear what you would expect in a major metropolitan city. Basically contemporary stylish clothes that fit in more subdued colors and stylish but comfortible footwear. Basically the same stuff I wear in NYC.
Suburban American tourists often stand (not that anyone really cares) because they dress like slobs. They wear cheap, illfitting, generic looking clothes they buy bulk at places like Target. Clothes that scream “I normally just throw this on after work because it’s comfortible and no one really sees me in my house”.
Would that be when you are down at the saloon?
Hmm. I’ll contact the Meteorological Office and suggest that they update their averages.
I’d appreciate it.
Of course! It takes them to Piccadilly Circus, to see the lions.
Not a Londoner, so I guess I’m not that qualified to answer this, but I think jeans are usually okay. As far as shoes go, though, I would definitely spring for COMFORTABLE. If you’re going to be walking around a lot, you do not want to kill your feet, no matter how cute your new shoes are. Wear the shoes that you usually do when you’re walking around in town, and if you get new ones, break them in first. Also make sure what you’re wearing is appropriate for the weather–don’t wear flip-flops when it’s gonna be cold and rainy.
Most people are going to recognize that you’re a tourist no matter what you do. I’m not against dressing to fit in, but don’t kill yourself trying.
Again, like everyone else, don’t worry about trying to fit in, blah blah.
But in answer to the OP, jeans and trainers are very common in london.
But the style of jeans is pretty tight, at least for women, like this.
It’s far less common to see london women wearing jeans as baggy as this.
Also trainers tend towards the ‘casual’ and away from ‘sport’.
This is just so you know: I’d recommend your wife wear whatever she’s comfortable in. Certainly don’t try to squeeze into highschool jeans or something 
Hope she has a nice trip
Hmm, on reflection, perhaps I may be guilty of observer bias 
[QUOTE=Lo-Slung Denim;12164301
Tourists stand out in London for reasons other than fashion, here are some reasons:
They talk to one another and to other people.
They usually have a backpack and/or camera.
They go to tourist attractions OBVIOUSLY
They look enthralled by London rather than jaded.
They look cleaner although dressed casually. This one I will qualify - I think that when Londoners look clean, i.e. pressed/ironed clothes, they are business clothes. When tourists come to London they might have bought new casual clothes to sightsee in. When not dressed for business or social occasions, a lot of Londoners look that little bit scruffy/shabby. Not meant to offend, I just think it’s true. Well, in my area anyway, which admittedly is not the best. I imagine it’s a bit different in High St Kensington.
[/QUOTE]
They use tickets on tubes rather than Oyster cards and wait until they’re standing in front of the barriers to find said ticket.
Once on the underground, they get off escalators and immediately stop to get their bearings.
They seem startled, then offended, when these actions cause Londoners to plow into the back of them, shoot them a death glare, then push past them and stalk off muttering obscenities.
On the topic of clothing, one of the things I love about London is the freedom to wear whatever you want without anyone judging you, or probably even noticing you. I was reminded of this just the other day, when going through Bank station at rush hour (tube station in for the financial district of “the city” - literally, the stop for the Bank of England), I noticed a long-haired Goth bloke in skintight PVC trousers and platform boots, striding through the bankers and city-types at 9am on a Wednesday. No one batted an eyelid.
Tell your wife and daughter to wear whatever they’re comfortable in (though some places, like the Orangery, may have dress codes they need to observe, so they should check them first), and I will try to avoid plowing into and glaring at any American women I see in March in case it’s them!
Oh, and Gyrate’s Hat is cool, I can attest to this…
That’s Washington DC, too. Funny how some things are universal. 
As everyone else said, she can really wear what she wants. She will still look like an American tourist, because she hasn’t been indoctrinated into the local style and she’s not dressed for work.
Anyway, it’s not the jeans or the trainers, it’s the style of them. When we wear trainers (sneakers), we tend to wear fashion ones, not ones you would do any kind of proper exercise in. We wouldn’t wear bright white ones.
We also wouldn’t wear waterproof clothing, hiking jackets, bright colours, hats of any description, carry rucksacks (back packs), cameras or maps, or any of the other things that tourists do. I’m sure your mrs might do any of these things, in which case she will blend in with the other how-ever-many-million tourists here. Unless she wants to look like she works here, which I’m sure she doesn’t.
Not necessarily true! I and lots of women I know have been coping with the winter weather with knitted beanies, baker’s boy caps, and the ever-popular fake-vintage cloche. I’ve seen a few fedoras on men floating around, but not as many as I’d like.
For colors, jewel tones are generally as bright as I’d go, and although I have lots of friends who carry cameras around, they’re usually taking pictures of pub signs or food, rather than, say, St Paul’s Cathedral.
