Hi Sue, it certainly looks like you have a problem here and there will be something that can be done to help you, without a little more info though it is difficult to assess what the solution will be.
From your post, your average calendar month income over the course of a year (ave 1175 per 4 weeks plus 2000 divided into 12 months) is around 1440. If you contribute £850 to the household pot per calendar month then you will be left with £590 on average. This doesn't take into account any ancillary expenses such as travel, general cost of living, food toiletries clothes etc so your true disposable income is likely to be a lot less than the £590.
I have always found that, as a rule of thumb, if your debts are spread across a range of loans, cards, catalogues etc, then you pay back on average between £25 to £30 per month per £1000 owing. Therefore, with £35k outstanding, even if you have some 0% APR deals, you will still be paying more than you can physically afford, thereby dragging you into the "robbing peter to pay paul" cycle.
There are other factors to consider here as well though. Are you a property owner? If not, is your partner a property owner and if so how long have you been living together? Are you both paying the same proportion of your income to the household budget? All these questions, and more, need to be addressed before an answer can be given, although I will stress, again, that a solution will be available to you.
I would therefore encourage you to seek professional advice as soon as you can and also to speak to 2 or 3 firms to get a balanced view. You can go to
WWW.IVA.COM to read some reviews on IVA providers on there.
Hope this helps and good luck!!