Afternoon Tea Manners and Penny Pinching

Wonderful little tearoom with tea, scones, sandwiches and it is a small book store too.
Tea and Tattle, it is across the street from the British Museum in London.
Check out the reviews on tripadvisor.
Not pricey and you may need a reservation. Check tripadvisor.

Hi,
I had gone to the Victoria & Albert Museum. They have the loveliest cafes I have ever been in.
Very affordable. Quite an assortment of foods: hot dishes, sandwiches, cakes and treats and of course teas. Check it out on the museum's website.
Have a fun time!

Afternoon tea and penny-pinching are not often mentioned in a sentence together!
Some of the teas in London are quite pricey!
The British Museum's cafe does a nice afternoon tea for about as cheaply as you can get one. Very good, also.
The V&A's cafe, as already mentioned, is another good place for afternoon tea. You buy individual treats. Just have a look at the selection up near the cash register when you go. A selection of scones, carrot cake, various cakes and cupcakes. Choose what you want. They will ring it up by item at the register.

Your question--whether you can still order afternoon tea for one person, and more than one eat from it--is "no".
Each person will be charged.
If afternoon tea is priced at 29 pounds, then each person who eats will be charged that.
The amount is per person.

Sometimes you will find a tea for couples that includes champagne.
The menu will say "49 pounds for two". In that case, yes the price is for two people to eat and drink.

You mentioned, "we will be two women and a pre-teen boy."
I think there is no limit to the amount of sweets a pre-teen boy can consume!
So I suggest you take tea at the Victoria and Albert Museum Cafe, where you or the boy can go back to the register to get one more brownie or cake as needed. It is not expensive there at all. And it's a lovely setting, with a domed gold ceiling.