ok well to answer your question yes there are two tea huts. The first is adjoining the Kings Oak pub and really caters for the families etc, drinks, food and ices, can't remember if it has seats inside but does outside.
The second option is across the green by the public car park, it's more of a kiosk but does have some outside seating, very popular. The area is very popular with cyclists, runners, walkers and bikers and I'm led to believe popular for dogs!
A very good pub for food is the Duke of Wellington on Wellington Road next to the golf course, bit poncey but decent all the same.
Can't make it tomorrow but maybe some other time, I'm in Royston, Herts but know the area well as I lived in Enfield and often used the area for "leisure" activities with girlfriends many years ago.