I think you have already made headway with the new 0% deal you secured, nice one! Others have also given you sage counsel. Please get all balances onto 0% deals of at least 18 months.
If you have an excellent unblemished credit rating, you should have no problem getting a new balance transfer rate. I've had higher balances than you for many years in the past, but I've never paid any interest, just the initial balance transfer fee if I have had to switch to another provider.
£400 per month on a £10,000 debt is not too bad, it's 4%. They key is not adding any more takeaways or holidays to the balance. £400 per month, with no interested increasing your balances would clear the whole debt off in just 25 months. If you cut your takaways in half and missed a holiday for one year, using all saved money to pay off the balance, you would probably clear it off in 18 months, possibly less, with a great weighs off your shoulders. Or, at the very least loads of spare credit limit to eat takeaways and go on a banging holiday!!! (Joke).
If you take steps to close any unused cards, then after 6 months of not having an account with them you will qualify for a new customer balance transfer deal. Also, log into some of your emply cards as they may offer balance transfer or cash advance rates at 0% interest for 'x' amount of months. I keep a few cards empty that always offer regular balance transfer deals, which is very handy when needed.
I think your key here is to cut down on expenditure for a period of time, make takeaways a rarer treat or pay from your bank account only. Definately ensure you get everything onto 0%. If you have any credit card that charges interest and you only ever pay the minimum, the card will never ever be paid off. Once upon a time, we went through the same situation. We cut out takeaways for at least 6 months and every time we fancied one, we withstood the urge and cooked at home, but more importantly, we would send an extra payment to a credit card for the value of the takeaway. This really accellerated how quickly balances cleared.
Good luck OP!