Back in 75 when I worked out of the site offices of Ham Dredging/V.O.W. Werkendam at Sutton Bridge Lincolnshire, a tealady went around serving tea from a cart to our desks. There was only about a dozen of us , but it was her full time job. I have never seen anything like that in Canada.
Is this custom still alive in Britain ?
I don’t know about the crazy world of dredging, but we had things pretty cushy at Barclays Bank operational HQ back in the '80s and even by that point there were no tea ladies with trollies. We didn’t even have a kettle.
I’ve seen it in Canada,but only once. Back in about 1979-1980 or so, I was working at a building in Toronto where the coffee cart made the rounds of the various floors. It had coffee, a few things like juice and soft drinks in a cooler, some sweet rolls and other baked goods, and–yep–tea. But I’ve never seen anything similar since.
When I was in London on business a couple of years ago, there was a tea dude. I can’t say for certain whether it was his only role - I imagine he probably worked in the cafeteria when he wasn’t doing tea rounds, but every day, he’d do his rounds with his trolley.
Of course, being a heathen American, I tried ordering coffee. He had it, but it was vile.
Sounds plausible for such a thing to still exist in Japan. Female labor was/is sufficiently cheap that it’s easy to have a pack of twenty of them around to do menial tasks. Banks there, for instance, are woman powered rather than computer powered. So instead of a couple people behind a counter, it’s a swarming sea of women running around making copies, bringing tea to the mens’ desks, filing stuff, looking stuff up, etc. Look up the history of the word “computer.” 
As upward mobility and the chance to stay employed after pregnancy rises, such jobs disappear.
Not in my office in London. She was replaced by vending machines.
I started working in 97 and have never seen a tea lady. Every office I have worked in had had a kitchen area, with free tea and coffee facilities, and you pop over and make your own when you feel like it. Sometimes people are in rounds, where you go when it’s your turn and make drinks for the entire group.
All but disappeared, IME.
I’ve seen that in old movies and TV shows et in American offices too. Apparently all the office workers had to take their coffee break at the same time, which was when the cart came around. I doubt if they still do that anywhere today.
I worked in a place once that had a tea lady who doubled as a cleaner. Probably replaced by vending machines now.
We have a Bangladeshi tea boy we share with some other offices. He also cleans the place and washes our cars. (We pay him extra for extra stuff.)
He is looked down upon. He speaks excellent English, Arabic, Pastu and Bengali, but he is paid less than the rest of us. Go figure.
This is my experience too. Only surviving examples I’ve seen are on Trains and planes. They might still use them on National Express buses, but I’ve not used them in years.
She gets a mention in this song though!
In the late 80s boom, I earned £5 an hour at the Equitable Life Assurance Society (yes, the one that went bust and ruined everyone’s retirement - the curse of jjimm lives on), and there we didn’t just have tea ladies who came round once in the morning and once in the afternoon, we also had an entire restaurant, with a full a la carte menu, cheeseboard, salad bar, the works, all for free - and if you worked beyond 5 a lady would call up and ask what sandwich she could make for you, and what crisps and chocolate biscuite you’d want. Good days!
I remember seeing the last one in KPMG in Dublin in 1995. Not seen one since.
The widespread presence of tea ladies was in many ways the result of efforts to improve war production in factories during WW2 (and were surprisingly effective in that regard). With that in mind, its no surprise that as the nature of the average British workplace has changed, their presence has declined.
That said, these days you’d still be hardpressed to find a workplace that doesn’t have some kind of tea-making facility, but it could be anything from company-provided facilities to some ad-hoc arrangement between staff.
Where i currently work, for example, a small kitchen is provided by the company, as is a huge range of tea bags, sugar and milk. The actual process of making tea however, is undertaken by the staff.
The role of making the tea tends to rotate round the tea drinkers in the office, with everyone taking a turn to keep it all fair. We tend to get through 3 rounds of tea a day (on average) which means each person ends up taking a turn at making it twice a week or so.
Among the books and equipment I lug from one school to another you will always find a pack of tea bags, so all I need is a mug, hot water and milk. 
Sometimes I’ve thought of packing in some of those catering-style milk containers for when the latter isn’t available, too, but I’ve never got around to buying some.
I’ve seen it in both the UK and New Zealand, in organisations where there is an in-house cafeteria, so it’s basically a trolley of the most popular items that gets trundled around the workplace.
In India, it’s common for office settings to employ one or more “peons” (invariably men) whose duties include making tea twice a day for everyone. They also run official and personal errands (for tips), including getting travel reservations, laundry, lunch (they usually are allowed to keep the change). Good peons are in demand and they were often head-hunted by other offices.
My sister-and-law tells a story about discovering that the peons in her office were using the milk supplied for tea to run a ghi (clarified butter) operation on the side. It was tacitly permitted as a perk of a relatively low-status job.
When I was at Bell Labs, late 70s / early 80s, they had coffee carts. They were pushed around by the staff that ran the company cafeteria, and delivered terrible coffee.
They still have tea trollies for the benefit of patients in hospitals in the UK, if that counts,
We had a tea lady - Jean from Northern Ireland - when I worked for London Underground’s Metropolitan & Jubilee lines in the mid-80s. She was a member of station staff who had been put on “light duties” due to some sort of illness. When she was off, her replacement was Olga who was born on Falkland.
In the early 90s, at the Patent Office in Newport, we had tea girls who provided mobile tea, coffee and even hot water remotely so we didn’t have to schlep all the way to the canteen.