Sorry for so many responses, but since I’m right here on the ground as an American tourist in the UK, I’ll try to help a lot. Regarding shorts, there is what is most like a local here at a pub wearing shorts. Newcastle doesn’t make it into most typical tourist itineraries. It’s 47 F/7 C
I am surprised nobody has mentioned “your best brown baggies and platform soles”. Maybe that’s only for South London.
There’s nothing out of the ordinary about shorts, sneakers, T-shirts, hoodies, sandals, running shoes, sweatshirts or hoodies. Here’s a photo of people in summer. Just be prepared for a range of potential weather in May, from a sunny 90 °F / 32 °C to a rainy 50 °F / 10 °C (or less if you’re in Newcastle).
The OP is in his 40s.
Oh yes! 
People in their 40s dress different from people in their 20s?
Not sure that makes much difference, and 40s is still young! Maybe older people are more likely to wear shirts instead of T-shirts, and less likely to wear hoodies. People in their 70s and 80s are more likely to dress like it’s the 1950s.
I’ve seen the admonition against wearing T-shirts in the UK more than a few times. I never know the background of the person giving that advice, however – how old they are, where in the UK they are from, or anything else.
Curious, though: for those in the UK who don’t abide T-shirts … what is their minimally-acceptable torso-covering garment for “dressed-down” casual wear? Polo-type shirts? Button-down short-sleeved shirts? The upper half of a football kit? 
Don’t you be knocking my cowboy boots!
I used to travel to Hull quite a bit for product certifications and would typically show up with a tan after prior weekends in the sun. Now THAT made me stand out!
That’s very strange. Maybe they’re older? I’m 43.
Other than t-shirts men wear button-down shirts (just called shirts in the UK, since we don’t use shirt as a generic word for upper half clothing - that’s a “top”) but usually long sleeved, rugby shirts, polo shirts, sometimes a jumper like a fisherman’s jumper or something. But I just checked through a few photos on Facebook and they’re almost always wearing t-shirts.
Same with women. Usually t-shirts, sometimes a blouse or shirt even if it’s casual, sometimes fitted tops. Also quite a lot of women wear dresses for casual as well as formal. So there’s more variety but all the same a t-shirt is still one of the staples.
For fellow Americans following along who might not already know, “trainers” are “sneakers.”
My question: What is implied by wearing jeans and sneakers? Or does it just mark you as a tourist?
And in Canada trainers and sneakers are runners, or more commonly running shoes.
She was talking about eating at a niceish restaurant, rather than general casual wear. Though tbh I think most places would be fine with jeans and trainers these days. I’ve seen jeans and tracksuits bring written for afternoon tea at Claridge’s!
There’s nothing wrong with jeans - I work in a design office, and would guess that 80% of the men and 30% of the women are wearing jeans right this minute.
Trainers are less common, particularly the big chunky kind. Instead, people would tend to wear leather/suede shoes or retro trainers.
What you need to remember about hanging around in London or Bath is that the locals are likely to be going to or coming home from work, or going out for a nice meal. Even if we’re working in very casual offices (as I do), we’re likely to be a little less casual than most tourists.
If in doubt, avoid bright colours (particularly in jackets), waterproof clothing, walking boots, large graphics on t-shirts and sweatshirts/hoodies. In fact, avoid hoodies in general - someone in their 40s probably wouldn’t wear one ‘in town’, even if they hang out in one at home.
Plenty of men get their legs out in shorts as soon as the weather dips over 16C, so I wouldn’t be too worried about that. They wouldn’t typically wear shorts to restaurants though.
Oh, and no baseball hats on anyone over 18 or not part of a street gang.
You’re still going to look like a tourist though - there are subtle design/fit clues which you just can’t avoid without a total makeover.
So, if I were going to the UK, the absolute last thing on my mind would be “what do I wear?”.
I’d wear what I would be comfortable wearing while on vacation in a given climate. If I “look like a tourist”, well, fuck me, I’m a tourist, so there.
Different strokes - the OP clearly feels differently.
I totally understand, I’m just surprised that as of page 2 there hasn’t been a comment like mine.
WTF!? So do Brits walk around squinting because they are too cool to be mistaken for tourists? I’m going to need an explanation on this. Sunglasses are functional for some people, like shoes. Right?
FWIW, Indiana Jones’s satchel was a British Mk. VII gas mask bag.
Exactly - it’s not so much “type of clothes” as cut, fit, color… American shorts don’t look to me like Spanish shorts, they look to me like Spanish bathing trunks. Which are fine streetwear at a beach town where everybody looks like a tourist except for those who look like they make their living off tourists; in a small inland town well, you’ll look a bit lost simply because small inland towns don’t get as many tourists.
Nobody needs sunglasses here, it’s usually raining, or it’s going to rain.