We had a similar 20k per day limit so transferred the money to our solicitor over several days. I think we also sent a small amount (£100 maybe) and got confirmation it had arrived before sending the big bucks.
That's another plan I had. We've already paid some up front for searches so have the payee details loaded. I will be confirming over the phone that the details are still the same then probably doing that.
We had a similar 20k per day limit so transferred the money to our solicitor over several days. I think we also sent a small amount (£100 maybe) and got confirmation it had arrived before sending the big bucks.