We are in a similar position op.
We have a mortgage, but the house we are in atm is just too small for us (was fine for me and dh when we were a couple but not so much with 2 dc). We have a VERY large CCJ (£18k!) on our credit file which will drop off in about a year. Although we are in an excellent position financially, have secure jobs etc, it makes re-mortgaging to move to a bigger house impossible. We just won't get accepted at the moment.
We considered selling and then renting but decided against it - I really don't want to get off the property ladder and risk a housing boom that would see prices soar over the next year or two, which would make it difficult for us to buy again.
So we've transferred our mortgage to a BTL and rented it out (tenants moving in Dec). The rent will just cover the mortgage and LL insurance, and we have about £2k set aside in savings, as back up money for if the house needs any repairs etc.
Regarding the Estate Agents 'not letting' to you because of poor credit. It's not always the case, and the credit checks that Estate Agents undertake are NOT as black-and-white (yes/no) as when you apply for a mortgage. Ultimately the LL will have the final say and can decide to take you as tenants whatever the EA says.
We have arranged a rental of a bigger house for us. We found one we liked, approached the EA and told them upfront that we would fail the credit check, but would like our 'case' to be presented to the LL anyway. We explained the circumstances of our £18k CCJ (which are very unusual and not a case of 'bad' or unpaid debt...there is a 'reasonable' explanation to it iyswim) and asked that they speak to the LL. We could easily prove affordability and 5 years worth of unblemished history with making our mortgage payments on time.
The LL considered it, met us and asked a few more questions, and then agreed to let to us. We still had to pay the credit check fee (which as predicted came back failed) but did not have to have a guarantor or pay rent in advance, despite failing the credit checking.
Disclaimer: I think our situation is more likely to be an option if the house has been empty a while and the LL is getting desperate. Our rental had been empty for 4 months and before we approached I think the LL was resigning themselves to thinking it would probably remain un-let until Christmas was over, so was much more open to considering us.