I've known quite a few self-employed people who don't have a business account. I'm pretty sure there is no requirement to do so, but the banks may be awkward if they conclude a personal account is being used solely for business.
However, in my view it is essential to have an account which is quite separate from personal income/expenditure as mixing the two up can make it very difficult to prepare the business accounts & tax returns properly. In particular, HMRC can become difficult if they are not satisfied the accounts are a true representation of the business.
Incidentally, have she registered with HMRC as self-employed & started paying Class 2 NI (unless she is exempt based on low income)?