How much interest are you currently paying every month? If you have multiple debts, it might be worth looking to a debt consolidation loan for starters. I've just taken one out, and have lowered my monthly outgoings by £300, which is fab. It will take 6 years to pay off, but the difference is that the payments are manageable, and not spiralling like they were before.
A few months ago, me and DP sat down together, looked at every single bill, and worked out where we could cut back. We decided we could do without a few TV and music subscriptions, we both lowered our phone contracts. We cut back drastically on takeaways and started batch cooking and eating the most boring foods imaginable.
As for transport to work, I'm sure you've thought of it, but are you definitely using the cheapest option?
Is there anything in your house you can sell on eBay/Vinted? Have you got the time for a side hussle? (I'm currently using an app that pays play time on mobile games, only get about £150 a month but that's super helpful at the moment. There are also a couple of decent survey apps that I can recommend. It's not amazing, but it can help you chip away at a little bit of the debt).
Also, before you make any purchase, think about whether you really need it. Anything you decide you don't need, but nearly bought, pay the equal amount off a credit card, or whatever, before you spend it on something else.
Debt is hard, really hard. But 10k honestly isn't the end of the world. I promise!
(PS if you have a really big mortgage, you might find that adding 10k onto that would be the best bet, spread out over the remaining term).