The overdraft has way too high interest rates can't you find a loan through a comparison portal that can then be paid off quickly with special repayments?
VW Bank e.g. 2.95% for a [frame credit] (revolving at any time and of course also fully repayable daily) - applies for the first 12 months from account opening.
Installment loan with the option to repay everything without penalty. Would only take it out if the financing of the house is complete. Alternatively, wait 3 months and then start.