He was feeling the need for a stick ever more strongly. On his release from hospital Charlotte had given him an elegant antique Malacca cane that she had claimed belonged to a great-grandfather. The handsome old stick had been too short for Strike, causing him to list to the right as he walked. When she had packaged up his things to remove from her flat, the cane had not been among them.
Once his leg gives out completely on the West Brompton bridge, Robin also recognizes he needs help:
Notice here that Robin's suggestion is that Strike buy a stick, but Strike buys it himself. When Strike gets in a cab (sans Robin!) to continue his mission in Chapter 26, he heads to:"Haven't you got a stick or something?"
Wish I had."
"We can get one. Chemists sometimes sell them. We'll find one." Then, after another momentary hesitation, she said:
"Lean on me."
"I'm too heavy."
"To balance. Use me like a stick. Do it."
The home of Elizabeth Tassel, took note of the route he traveled and would have arrived in a mere four minutes had he not spotted a Boots. He asked the driver to pull up and wait, and reemerged from the chemists shortly afterwards, walking much more easily with the aid of an adjustable stick.
Interestingly, both sticks reappear, as so many elements do, in the even numbered books. However, in later mentions, there is an important change that may or may not be a simple error. In Lethal White, at the restaurant with Charlotte, she picks up the adjustable stick that has fallen to the floor.
"Where's the cane I gave you? The Malacca one?"
"You kept it."
"Who bought you this one? Robin?"
Amidst all of Charlotte's paranoid and frequently wild accusations, she occasionally made uncannily accurate guesses.
"She did, as a matter of fact."