Have we paid a mortgage payment twice?

[Mortgageconfusion123]

We've just remortgaged, we came to the end of our fixed interest period (December 1st) so have gone to a different lender.
We paid NatWest £921 on December 1st, we completed new mortgage on December 8th (should've been 1st solicitor cocked up)
Our ongoing mortgage payments with new lender will be £1472 on the 8th of each month. New lender is saying the first payment will be £2403 to account for interest in December.

NatWest say mortgage payments are always taken in arrears so the December payment covers us for November. So why are new lenders asking for December in arrears and seemingly January in advance all at once? We've moved lenders before and never had this issue.
Having said that we've never used the conveyancer we did this time and it's been a nightmare.

Some lenders charge in advance. You haven’t paid your interest since 8/12 so this will be added to your first payment. It will be in the terms and conditions and is called initial interest. You might have an option to change your due date if this is not something you budgeted for.
I would call your new lender to check your options.

For anyone searching and this comes up, NatWest were wrong, they ended up refunding party much the entire last payment they'd taken. So whilst we had a double payment in January it meant we hadn't paid in December so it worked out.