Citrus maintenance

I have a lemon and a lime citrus in my conservatory.

I put these outside during the summer months, and before bringing them back in, I clean up the plants, prune them and spray them with an insecticide, also getting rid of existing scale insects.

However, shortly after bringing them indoors, the leaves and branches begin to exude a sticky 'honeydew' type deposit, which also drops on to the floor around the trees, and is difficult to remove.  I have tried removing the deposit with soapy water, with limited success, and it doesn't appear to be related to scale insects which inevitably appear later.

Any ideas on how to deal with this deposit effectively would be welcome!

Wendy Draper