The price per unit and daily standing charge won't increase, but they can increase your direct debit if the amount you use is higher than the amount that the direct debit was based on.
This is an important distinction that many fail to understand. Utility company tells you they'll supply your G&E for £80 pm and send you details of their rates and set up a DD for this amount. After you've given them a few readings, their algorithm tells them that you use more than they thought and they want to increase your DD to account for the debt that's built up and to keep up with usage going forward.*
Customer feels conned and upset because the payment they thought wouldn't increase has done.
This is an important point. Companies will point to OFGEM's requirement for them to review customer DDs regularly but the cynic in me says they also like a nice buffer in their bank account in case of any defaults. For anyone switching now, which is going into the Winter, DDs are unlikely to cover bills because the DD averages out over the entire year but you're going into a new contract at the highest usage part of the year.
I get round this by giving a monthly meter reading, calculating what my usage was (if the company doesn't tell me, although several do monthly billing including Octopus and Eon) and paying the balance if it was more than my DD. But that relies on having the money available to make the additional payment, which I appreciate not all do.
By making sure my balance is always zero or slightly in credit (which accrues over the Summer months) companies seem to be happy with keeping my DD value down.