I was in the same situation as you last year (no SWs) and I still managed to secure summer internship in S&T.
Your work experience seem diverse and quite relevant, so this summer just try to do something relevant to boost your CV, e.g. accountancy, finance ...
Last summer I did internship in small management consultancy which is not that relevant to S&T, but from every work experience you can get something to talk in your interviews.
As for general tips: apply as early as possible (august, september), start researching your area of interest in depth (helps with comp questions and interviews, learn any technicals necessary), practice numerical/logic test if you need to (assessmentday is a good website), build on your commercial awareness.
What uni are you?