Yes, Katrina, you will be entitled to some Government based statutory sick pay. As Zaf mentions, go onto a Government website... I found "directgov.uk" invaluable. The job centre will also help you make a claim. In the meantime, the Jobcentre plus can also help you make a claim for additional benefit as the Statutory sick pay won't be a lot of cash. As Zee also mentions, you most probably will be entitled to a crisis loan to tide you over with money while you wait for the claims to be sorted out. Often it will take up to four weeks, if you hassle them. Having children will entitle you to a bit more financial assistance. All this is assuming you do not have another income coming in from a partner. Lastly, about your rent, if you're entitled to dwp benefits, you will definitely be entitled to some housing benefit. Again, the Jobcentre Plus will advise you how to make that claim.
As for your depression. We all need time to help recovery. Anti-depressants usually take up to 3 weeks to take proper effect. However, personally, I usually feel better after 1-2 wks.
Hope this will be of some help.