Even a 'really tiny garden' is likely to be as big as the recommended minimum run size, so I would just let your bunny enjoy running around in the space you have. It is much more natural for him than trying to get him to 'walk' on a lead and he's likely to get much more exercise doing that than being confined to maybe half an hour on a lead every day. Rabbits don't really walk on a lead in the way dogs are trained to. They randomly run in zig-zag patterns, binky, jump up on things..or just sit and contemplate.
Walking rabbits in public on a lead could also be quite hazardous. Apart from the possibility of diseases from wild rabbits (which you should be vaccinating for anyway), there is the chance of escape (harnesses don't fit that well with a spooked rabbit trying to escape, and leads are easily chewed through), dogs which will certainly not ignore a captive rabbit (ie pretty much any dog you meet) and other hazards and predators (including people, bicycles, pushchairs, etc) which could easily cause harm / stress to a rabbit.
There is someone who walks a cat on a lead in our nearby woods. I am always wary for the safety of the cat and have to do a big detour with our dogs for the safety of all the animals as I have no doubt that I would be unable to stop the dogs going for that cat - and ours live with lots of cats and other small furries. I dread to think of what could happen to a rabbit in a similar situation. Just picking them up not only doesn't keep the pet safe, it also puts you at risk of attack as well.
Have you thought about getting a companion rabbit? Then they both get more play time chasing each other round in whatever space is available, and are less reliant on humans for company and exercise. As long as they are both neutered several weeks before any introductions, bonding need not be too difficult.
