Help! Serious white fly problem!

Hi there,

I'm a complete amateur gardener living in a rented property with a small courtyard garden. A large plum tree overshadows the court yard and is completely infested with, from my research, looks like whitefly. I took to the tree with pruners and cut down as much as I could but, in doing so, I seem to have disturbed the bugs and they are now in the atmosphere everywhere. This may have been made worse (or better ?) by the very heavy rain over the last day. 

 The white bugs are now falling from the tree in swarms. I actually cannot go outside without being covered in them. The patio almost looks like it has a vague sprinkling of snow!  I believe this is called tree dandruff. I caught a few bugs on a bit of paper and from what I can tell they are possibly dead, but,  over 24 hours later, they are still falling.

I'm really not sure what to do? Is it a good sign or not that they are coming off the tree?

If anyone has any advice I would be most grateful. I just want to be able to hang my washing outside again!

Many thanks for your help...

Regards,

A desperate gardener