"banks will only lend to SOEs or big private companies"
Banks' prefer to lend to SOEs or larger companies, sure, and those customers get the best rates. Credit _is_ available from banks for smaller businesses, but banks' role in this lending is a little different than in the US/UK.
A bank making a small business loan in the UK is serving two functions: (i) providing capital, (ii) taking on credit risk. In China, many small business loans are granted by banks (and live on a bank's balance sheet), but the credit risk is taken on by a credit guarantee company.[0][1]
The small business will pay interest to the bank, and fees to the guarantee company.
"there isn't much credit for small private companies"
There is, it's just that (i) when banks lend money sourced from their wealth management products (理财产品) , it doesn't show up on banks' balance sheets, and (ii) there are other non-bank lenders.
Search for 'wenzhou rate', 'shadow banking' or 'china wealth management' if you're interested in more detail, e.g. see the 'wealth management' section of this paper[2].
[0] http://www.ft.com/cms/s/0/2653ed8e-21a2-11e0-9e3b-00144feab4...
[1] http://www.wsj.com/articles/next-up-for-chinas-central-bank-...
[2] http://journals.sub.uni-hamburg.de/giga/jcca/article/viewFil...