First time renting

Me and my partner have two kids, have lived at my mom's the passed 4 years, we financially contributed to everything.

Now things are getting intense so we're looking at properties and have a meeting with the estate agent on Tuesday, I'm not sure what to expect. Thing is, my partner gets paid cash, there is no payslips, it is legal but his only contracted 25 hours which is around £855, but he works 40-60 hours so total income is around £2000 a month, also we are signed up for government assistance which we get regularly, we report the income ourselves with no proof, never have lied though so for a little while we haven't recieved much, but I've already spoken to them and they have confirmed once I inform them of my new rent and expenses, there could be more help if required.

But I know not all landlords accept government assistance, but I also know they don't have to know because I can choose for it to get paid in my bank account to pass on.

I doubt we will need it, from my calculations (not sure if it's relevant but Im an associate accounting technician member, have the qualifications just don't work yet) we will be able to afford it.

His boss has agreed to be a reference for us, but we need another one, preferably our last landlord, could my mom be one as we pay rent or would it be a conflict of interest and biased?

We have never taken out anything on credit and have no debt so she has also agreed to be our guarantor if we required one, would this help the fact we have no physical proof of income?

Are we allowed to show bank accounts?

I'm just very nervous, trying to manifest this house, it's literally perfect 🤞🏻

Any advice appreciated