If you owe £25k and are trying to borrow more then lenders will assume that you aren't going to pay off the cards and it is just additional borrowing. Unless he is earning significant money then you are not going to pass affordability criteria.

Forget about loans, you wont be able to borrow your way out of the debt you are in. You cannot do the 0% shuffle and not have a plan to pay it back at some point as you have found that the deals run out and you run out of credit.

What did you spend the £25,000 on, can you sell anything that you have bought? If its day to day spending then you have bigger problems to overcome.

List out the cards and interest rates and minimum payments along with your SOA and see if you can reduce your lifestyle to pay the highest interest debt first.

Your "good" rating is nothing to do with the fact that he will not pass the affordability to the lenders.

You cannot borrow your way out of debt, so please stop trying to, all you are doing is digging a deeper hole. There is a good reason why there are a huge number of people on here who are back for a second or even third attempt at debt-busting, and that reason is generally consolidation. It rarely works.

In my signature you will find the link to the SOA (Statement of Affairs) calculator we recommend on here - get yourself together a years worth of bank & card statements, sit down and fill in the calculator - it needs to be an open and honest reflection of how things are in your world right now. if you then "format for MSE" at the end, you can post that into a new thread on the Debt Free Wannabe board and we can take a look, and hopefully pick up on some areas where savings can be made.

Re the existing CC debt - first thing to do is to actively step back from using credit for day to day expenditure - that needs to be budgeted for and paid for from income. You can also join the MSE credit Club and use their eligibility checker to establish whether you may be able to get 0% Balance Transfer cards to get some of the debt at least onto an interest free basis. The vital thing here is that you MUST keep a clear note of when the 0% period ends and absolutely do NOT spend on these cards. As you clear a card by balance transferring or paying off the balance close the account immediately afterwards. As for the 0% cards themselves, cut them up on receipt - don't be tempted into sticking them into a purse or wallet. You may want to keep one card for emergencies, until you have a proper emergency fund saved up - however this again should not be carried around or used other than in extreme circumstances.

Step 1 - do the SOA
Step 2 - learn to budget and live within your means
Step 3 - get debt onto 0% if you can.
Step 4 - the long haul of paying back what you owe.

Firstly the pair of you need to stop worrying about your 'score' - it's just a marketing tool for the credit reference agencies and not relevant to the real world.

The easiest way to keep interest low on credit card debt is balance transfers

https://www.moneysavingexpert.com/credit-cards/balance-transfer-credit-cards/

after first using a pre-eligibility checker

If you are no longer being offered these and can't meet the minimum payments then the red lights are flashing and you should head over to debt-free wannabe and post a statement of affairs

https://www.lemonfool.co.uk/financecalculators/soa.php

As EH says you really need to look at your spending and cut back which is what an soa would do.

Lots of alarm bells in the OP. Heaven forbid the husband losing his job for whatever reason. Do you have an emergency fund at all? It's not good to bring another child into the world if you are already struggling to cope with two.
You need to fill out an SOA, attack the debt head on between the two of you and prepare for a bumpy 2020.

Your husband should stop blaming you (or your credit score) and think why anyone not making significant inroads to £25k debt should be considered a good risk by another loan company.