Not always are caterpillars found on the ground. Occasionally, you can find some on the height of one’s eyes. But that’s not all, it may also be worth to have a look up.
The White-letter Hairstreak spends almost all of its life high up in elm trees. This includes the larval stage, therefor it’s possible to spot the caterpillars by standing right under the leafs of a tree. Then, have that look up to the bottom side of the leafs. This may requires a sunny day to get a good look. Some twigs hang almost down to the ground (see photo below), making it possible to get a close-up or collect a caterpillar for raising.
If you want to raise the species from eggs here’s a couple tips for tracking them down in winter.