That is a bad infestation of aphids on your ivy.

Squish them, then repeat every several days.

Or spritz them with insecticidal soap diluted according to label direction and, then, repeat according to label directions.

You can squish them between your fingers or you could knock them off the Ivy with a strong stream of water, it is not necessary to use Insecticidal Soap although that can be used as well. You will need enough force in the water to knock the wee buggers off the plant.

The Aphids you knock off the plant will not return but a new generation is already there waiting to move into the vacancy you will create so be prepared to see more in a few days and weeks. Aphids produce live young almost as soon as they are produced so you probably have several generations of them standing by.

kimmq is kimmsr

What fun!

If I get rid of them are they likely to return? How would they have got to the plant in the first place? I presume they must have been on it when I bought the plant.

Aphids have a flying stage when they are mobile, so could have scouted your plant out. Or they came with the plant, as you suggested. That happens a LOT!

Once you get this population under control, you should probably inspect your plant every once in awhile for its entire life. Aphids are pesky little creatures.