Remortgage completion date after usual payment date

I am remortgaging and have been given a completion date of May 2nd, with a set redemption figure.

However my current mortgage direct debit is taken on the 1st of the month so I am worried an extra, unnecessary payment will be made.

Should I cancel my direct debit now so the payment definitely won't be taken, or risk having to get a refund? I can imagine having to spend a long time on the phone or going to a branch to get it back!

If it matters, I have made several overpayments this year.