However, despite the limited space, marauding foxes, a northerly aspect and a pair of overhanging sycamore trees which suck the goodness from her soil and have had a preservation order slapped on them, her garden, especially at this time of year, is a glorious profusion of foliage and flowers. Cullinan, 80 in August, created the garden with her late husband in 1980, when they moved into the terrace house and were presented with a patch of weeds and 21 sycamore seedlings.
There was no grand plan, she recalls. They took paving stones from the Hackney tip to fashion paths and later on, Cullinan and a friend picked bricks out of skips and made the low brick walls that edge the beds and borders.
"We worked our way down the garden creating different areas and when there wasn't any more room, we had to go up." Going up included not just a pergola which is now garlanded with roses and clematis, or lining the fence and walls with horizontal wires, but installing a series of freestanding poles here and there and topping them with bicycle wheels laid flat. "The grandchildren are always making bikes so they've always got bits of bike, and we thought we'd use these as hoops for clematis," she says.
That her overriding passion is for clematis is easy to see. Somehow, shimmying up the pergola, weaving their way through the spokes of the bicycle wheels to make flowery parasols, there are more than 30 of them, mostly in sumptuous shades of blue, regal purples and deep clarets that tip into near-black.
Cullinan dismisses the myth that clematis are prima donnas. She feeds them B&Q's cheapest plant food, tidies them up in autumn and is happy to share her pared-down pruning methods: "Pruning is a cinch. The ones that flower early, you don't touch. The ones that flower halfway through the year, you halfprune them. The ones that flower later in the year, you slaughter them down to the ground at the end of February. It's logical when you've got the idea."
Every clematis in her garden started life as a small plant, because half the fun for Cullinan is raising them herself. "A good friend lives near Stone Green Nurseries in Kent, and I buy them small for £3.50 each. I nurture them, and a year later they're as big as the ones you buy for £15."
Her style of cottage gardening — giving plants priority, and growing them cheek by jowl — is reflected in the way she brings plants in. She has grown most of them, clematis aside, from cuttings, including a bountiful Fuchsia magellanica, perfect box spheres and a phygelius that produces a mass of tubular lemon flowers. "It's such a ball, money for jam!" she says. "You just take the cutting, pull some leaves off the sides, prod it into some compost, stick a plastic bottle over it, leave it for a few weeks, and Bob's your uncle."
Ask Cullinan which clematis is her favourite and she says: "They're incomparable." When pressed, though, three figure highly: Romantika, with purple blooms, Mary Rose, which has double flowers of a dusky mauve, and Clematis Etoile Rose — with curved-back cerise bell flowers — that tangles into soft-pink rose High Hopes.
She also grows a wonderful herbaceous clematis, Durandii, which in everybody else's garden performs as a herbaceous plant but for Cullinan, who insisted it grow up the pergola, it did, of course, oblige.
Tigger Cullinan's garden is open to visitors by appointment. Contact her at firstname.lastname@example.org