Barb, when she scanned this postcard, put the date as January 2, 1908. The January part is not quite clear to me, but it could well be that the Farmers were visiting the Grays in Sevenoaks over the Christmas holidays, and that Kathleen chose this postcard because it gave a feel of the winter’s walk that she took.
Kathleen sent the postcard to her father's place of work, so I guess he wasn't living in very memorable quarters while he waited for his children to finish their education so that they and his wife could join him in Savannah.
And why didn't Kathleen write anything in the message area of the postcard? I have no idea.
As for Wildernesse Avenue, the Wildernesse has a website: https://www.wildernesse-estate.co.uk/history It says:
In 1705, the estate was bought by John Pratt, a future Lord Chief Justice and later Lord Camden, who extended the estate as far as what is now Sevenoaks Hospital and also to the north of Seal Road, making it more than 500 acres. The Camden family, who owned the estate for more than 150 years, also gradually enlarged the house. Wildernesse Avenue was made the principal drive for Wildernesse House. It extended down what is now Hillingdon Avenue to a lodge which still stands. In 1795, the first Marquis Camden had been Lord Lieutenant of Ireland and Arthur Wellesley, later Duke of Wellington, had been his ADC. In 1815, just before the Battle of Waterloo, Wellington visited Camden at the estate. A great avenue of limes, known as the Waterloo Limes, was planted along Wildernesse Avenue to commemorate the occasion. Wellington visited again 1832. The avenue of limes still exists.
and Wildernesse Avenue ran through the Waterloo Limes down the route to Wildernesse House from Seal Hollow Road.
But, unlike Aunt Alma, I am not a botanist, so I do not know what sort of trees the limes are. I mean, they couldn't grow actual limes in the London area, so what are they?
Mid 2025 note: I've been rereading the novels of Angela Thirkell, which Aunt Alma loved, and I find occasional mentions of limes - for example: "From the house the ground, bounded on its far side by a row of tall, clipped limes, like a fortress wall, fell away towards the river." (From The Duke's Daughter.) So the trees in the postcard must be the Waterloo Limes, but why are they called limes?