I think you are somewhat confused about the rules regarding this.
I am advising the OP to genuinely separate her household from that of her partner, not her relationship to him.
This is all that is required to make a genuine claim for UC and other associated benefits for a one parent household. There is no fraud involved at all, and financial hardship is a valid reason for this (in fact no reason at all is required).
There is no requirement for her not to have a relationship with anyone who is living outside her home, nor anything to prevent a live-out partner visiting during the day, helping jointly with the children in the home, eating meals when visiting or staying overnight occasionally. It is by no means fraudulent or attempting to be.
Here straight from the government website:
Definition of a couple
The Department for Work and Pensions counts 2 people as being in a couple if they live in the same household and are:
married to each other
civil partners of each other
living together as if they were married
The rules regarding UC and Child maintenance are published on the government website and it is very clear it is disregarded as income.
I can assure you it is very sound financial advice, and will substantially increase the OP's income, (even taking into account the cost of her partner renting a room in a separate house); and put both of them in a much more stable and robust financial position going forward. In addition the OP can continue with her maternity leave for up to three years should she wish to, without any loss of benefits or conditionally on returning to work in the meantime.
Once she is on a more stable financial footing after that time, there is no reason her partner can't return to the family home and continue as before. Absolutely nothing fraudulent or illegal in this scenario.