High tea

You want to look for "Afternoon Tea" rather than "High Tea". Can you have dairy? Traditional afternoon tea tends to be full of eggs and dairy (cakes, scones, clotted cream, tea sandwiches with egg salad, salmon, etc.), so you may be better off looking for a place that has a vegan afternoon tea so that you have some variety.

Here's one of many online lists. The prices of these places are well beyond my budget, but the first one (Browns Hotel Tea-Tox) looks like they would understand your dietary needs. You can e-mail them if their online menu is not more specific: http://www.telegraph.co.uk/travel/destinations/europe/united-kingdom/england/london/articles/Londons-ten-best-afternoon-teas/

K out the Wallace Collection museum and cafe .
Wonderful, reasonable and a museum to view after. One of my favorites.

Take a look at Forum and Mason and The Wolsely and see if they offer vegan afternoon tea. You may have to contact them directly and when making a reservation in advance, you must advise them of needing a vegan afternoon tea. There are places that serve vegan afternoon teas and you may want to google that to see who offers vegan afternoon teas. Also Neal's Yard near Covent Garden has restaurants that may be vegan and is vegaterian so you may want to look at those restaurants too. Maybe not for afternoon tea but in general to have a meal. Any hotel or restaurant that you see on this forum advising about afternoon tea and there have been several discussions regarding afternoon tea recently, take a look at their websites and if you don't see a vegan tea contact them and ask them if they offer a vegan tea. Just because you don't see it doesn't mean they don't have it.

You must make a reservation for afternoon tea before you go to London to insure you get a table.

I am going to London later this year and want to have an afternoon tea myself but not a vegan tea so I have been reading the forum with great interest on trying to figure out where to go for my afternoon tea.

Thanks to all for your help, will google afternoon tea. also im vegetarian so dairy is ok.... partial to desserts, which i know are made with eggs & butter. (yummy) but do not eat eggs in salad or omelet etc.

Then you do eat eggs in cake? If so then it won't be that difficult. You can probably go to a traditional tea and just ask if they can swap out some of the sandwiches.

https://afternoonteaonline.co.uk/good-for-vegetarians/

The link above should provide the information you seek.

High tea is an evening meal served with meat. Afternoon tea is with, scones, finger sandwiches and pasteries along with a pot of tea.