To sell or rent out, impact on t/c?

Hello peeps, I live in a mortgaged property and plan to move and rent something bigger as I have two disabled children and we are in desperate need of more bedrooms to minimise distress to them.
I would like to buy but my credit rating is rubbish and I can't see me getting a new mortgage easily, my current lender no longer do mortgages.

If I sell and have some money from the sale of the house how will this impact my tax credits?

The other option is to rent this out and then rent a bigger home, how will this impact my tax credits?

I'm not a money grabber I would just like some info with the best options. Thank you :-)