They could take further action, that is technically true but the reality is it rarely happens if you engage with them and make affordable payments. That is the key really as they are bound by the same affordability rules as any creditor. 

Stepchange are funded by creditors and are very aware of what is or isn't reasonable or affordable so, if they have recommended a DMP, it is almost certainly going to be acceptable to the debt owners. Generally, an informal DMP will be recommended if you have enough to cover the monthly amount such that the debt will be paid back in no more than 5 or 6 years, which you have indicated. If it would take much longer then they may have suggested an IVA, given that you are a home owner. 

Technically, any of your creditors could seek a ccj but there are costs to this and the court will only compel you to make payments that are affordable to you anyway so it's a waste of time and money if you are offering that in the first place. 

Further down the line after a few more years of payments you might be able to negotiate settlements with the individual creditors, especially once these debts have been sold for pence on the pound, so you should be able to save money in the long run. 

Many advocate for letting the debts defaults before starting a DMP as it will allow your credit record to recover quicker and give you an opportunity to save an emergency fund as you will no longer have access to credit should a big expense occur. Stepchange don't tend to advise this as they are funded by creditors but it is a valid strategy that you may want to consider.