Traditionally in the UK, the snowball method is used to mean starting with the most expensive debt and concentrating on paying that off fastest, while only paying the minimums on cheaper debt, although some people are using the US description which starts with the smallest debt. If you start with the highest interest rate, it will get you out of debt faster, although psychologically it can feel like you're getting somewhere and simplify admin if you pay off any smaller debts so say if you owe £8000, £5000, £4000, £400 and £150 you could pay off the two smaller ones first, then concentrate on the other three.
To add to the above, if you have any empty cards, see if they will accept you for a balance transfer offer - these are often easier to get if you already have an account.
For any interest charging debt, pay £1 more than the minimum. Either have it on DD for the minimum payment and manually make a payment of £1 each month, or you could pay it off by a standing order for the current minimum, which will be higher than the actual minimum when the balance reduces. This removes the minimum payment marker from your account, which makes you look better to lenders.
If you do get any low interest offers, just pay the minimum plus £1, while the debt is cheap. You can likely transfer it to another offer if you still owe money when the offer runs out.
Use an eligibility calculator to look for offers you might be accepted for and even if the chance is low, apply. If you're rejected,repeat the process every 6 months, as you might be accepted in future, especially as your debt reduces and if you build up a history of paying more than the minimum.
Review the rest of your finances to reduce bills and unnecessary spending, cancel unused subscriptions, see if you can earn or make extra money etc, to get out of debt faster.
For the mortgage, you can probably get a new deal from your existing lender without a credit check, so should be OK for that.