To have been overpaid £10k in a year, you must have been getting almost £200 a week in CTCs, OP. Were you getting working tax credits as well?
Tax credits are always provisional, based on the income in the previous tax year. A big pay rise, or starting work, can lead to a big overpayment if it's not reported (or, if it is reported by HMRC failed to act on it). It's usually adjusted in the following year, when they know how much you've earned.
I'd challenge this and ask them what income figures they're using, then check them against yours and your partner's P60s for 16/17. If it's wrong, tell them.
Sometimes they do historic calculations if it turns out that income information comes in ages after the year in question. I've come across it a fair bit in cases where one partner is self employed, and they're late filing their self-assessment.
If you can get an appointment with a welfare rights adviser at CAB or similar advice agency, I'd go and see them when you get the figures if you can't fathom it out. They should be able to calculate what the correct figure should be.