Benefits Question

Hello!
I have a question which is mostly related Housing Benefit/Local Housing Allowance, so I know it may not be able to be answered, but I genuinely don't know where to turn, so I thought it might be worth a go. (But apologies if it's inappropriate to ask here!)

I get ESA and PIP as well as Housing Benefit.
I am single and live in a privately rented one-bedroom flat.
My landlord has just landed me with a rent increase of £150 per month, which I can't afford in the long term.
However, I am also pregnant.

My understanding is that once I have a child I will be eligible for the 2 bedroom rate of Local Housing Allowance, but I can't seem to find clear information about whether I would be able to stay in my one bedroom flat but receive the 2 bedroom rate of Housing Benefit.

The Entitled To website says that the number of bedrooms you actually have doesn't matter - for example, if you are entitled to the 3 bedroom LHA you could still get Housing Benefit for 3 bedrooms, even if you only have 2 (www.entitledto.co.uk/help/local-housing-allowance).

However, I just did a live chat with the CAB and they told me that I couldn't claim two bedroom housing benefit unless I moved to a two-bedroom property... So now I'm completely confused!

What I would like is to stay in my one-bedroom flat with my baby, but receive 2 bedroom rate housing benefit (which would mean I could afford the rent increase), but I just don't know which information about whether this is possible is correct!

Does anybody have any info? Or any ideas about where I could go to find out for sure?

Thanks very much!

P.S - I know that I will have to report a change in circumstances and this will trigger a change to Universal Credit, but I think the Local Housing Allowance rules should stay the same, even if I move to UC?