Have tested the water using test strips to check for nitrate/nitrite/ph
level etc but everything seems within the levels stated for a healthy
pond.

Algae isn't the sign of an unhealthy pond.

Have got several pond plants growing in an old washing up bowl ready to
be put in the pond but I want ensure that the water is safe for them
first. I put some in last year and they died within a few weeks.

You think algae had something to do with that? It shouldn't. Are
these plants entirely submerged? What kind?

Anyway, how may liters per hour does your filter process?

What's this pond made out of, and what's on the bottom right now?

C//