Hello there from another UKMember. Have you any pics of the pond?..... that would be good as we all like to see what's being talked about, far better to have a visual rather than just a mental pic, as sometimes we can get it wrong!
Plants are good for ponds, mine Is well planted despite having two large and boisterous Koi. I was going to suggest at least a couple of water lilies, as they not only shade the water from sunlight, which kelps to promote algae, but also provide a canopy of leaves for the occupants to shelter under from the suns rays or predators. However, I then re-read your post and saw the max depth is 1.6 foot. Many water lilies prefer much deeper waters, but, there are mini ones too. I would suggest you make the suppliers aware of the depth if you decide to get a lily or two as they may be able to suggest which (if any) varieties could be more suitable for that depth as a regular deep water lily when planted in a lily basket that is around 8inches deep will only have10 or so of water above the soil which isn't much really.
Elodea is a good plant for our UK ponds as is Hornwort and Starwort. Marginals like Marsh Marigold, Siberian Iris, and Pickerel Weed also help to utilise excess nutrients which all add to the green water syndrome. Hope this is of help.