Hey OP!
Okay so I work for the NHS and am currently on mat leave.
My understanding is that we get 8 weeks full pay, 18 weeks half pay plus SMP, 13 weeks SMP and 13 unpaid.
I chose to spread my payments over the 12 months. Sounds like you did too?
I've also had issues with payroll throughout my whole time with my Trust (one month the bastards just forgot to pay me, and had the cheek to ask whether I could wait till next month! Apparently my mortgage fairy pays my mortgage...)
I asked for a pay projection multiple times and was fobbed off each time. When they eventually sent me my projections they also didn't stipulate that what they had projected was GROSS not NET pay. So the first month I was £300 down. When I queried, only then did they explain the above. A bit like you, first baby, trying desperately to budget, I was devastated that it hadn't been made clearer to me. Turns out they don't made deductions because they can't predict them.
If they'd looked a bit closer they would've seen that I am salaried, don't do shifts, work 8-4 five days a week. Didn't think it would be that hard seeing as they caveat everything with 'this is an ESTIMATE'. Now I appreciate an estimate may be a few quid different, not £300.
Anyway, as it was, I've had to cancel my pension for a year so I can recover that money.
Before a career break with the same Trust, my manager forgot to tell them I was on a career break. They overpaid me 2 months wages and when I tried to send it back, they said to wait because they needed to check shift allowances. They eventually accepted the money 4 months later, and then started to try and sting me for pension/tax (£200). I never got to the bottom of it but argued the toss and eventually they dropped it.
However, that is an awful lot of money to have to pay back. I can understand the confusion but ideally you should've queried it when months down the line you were still receiving full pay.
Payroll in the NHS are renowned to be shit. I've had issues in all three trusts I've worked for. They can't leave you in hardship though, I would suggest contacting them as they will be able to sort out a more affordable payment plan.
My friend had her student loan refunded multiple times which wasn't explained to her (long and involved story) so they let her pay the overpayment back in manageable installments over 18 months.