I get a red 'x' when browsing this page so I cannot comment much. If you think it is overwatering, try touching the potting mix with your fingers ti see if it feels wet. Or get a moisture meter to measure the amount of water in the soil. Switching to bigger pots sounds reasonable at some point. Putting them out in bright shade outside in a place where it does not get exposure to lots of drying winds.

Thank you for responding but I hadn't realised the photo wasn't visible. It's fixed now and I would appreciate your opinion. I know red is often a sign of overwatering which is why I thought that might be the cause, but I'm not familiar with hydrangeas so it could be something else.

It is most likely Cercospora leaf spot. Very common with young hydrangeas and those grown in greenhouses. I would assume your cold frame provided the same sort of atmosphere as a greenhouse - lots of moisture/humidity in the way of condensation.

In the open and planted in the ground, these will most probably grow out of it. It is much more of a cosmetic issue than it is a truly debilitating disease.