Is this a May Fly?

Lots of butterflies were out this morning, including the first Painted Ladies and Marbled Whites that I have seen this year. But this delicate creature needs a name. It does not seem to have the long tail of a May Fly, nor the very long body of the Damsel Fly. Can anyone identify it please?

P.S. General consensus is that it is a Lacewing, what a lovely name. Thank you, my blip friends, you are such knowledgeable folks.

Yesterday's roaring stream has been topped up today, more heavy rain this afternoon and so it goes on.