I have an Ancol harness for my 6 pound boy. I got it in the smallest size & it fits fine if I adjust it down to nearly the minimum. It only cost £5.99 & comes in several colours.
However, this was too big for my littlest girl so I had to get a puppy harness. I'm sorry, I can't remember the make as she's had it a while & it doesn't have the brand on, but it has little coloured dogs & "puppy dog" printed as a pattern all along it. It has a detachable lead which is adjustable....at it's longest it is about 8 foot
& came on a card with two toys, if that's any help.
It was the only thing I could find small enough after searching all the pet shops in my two nearest towns