The closing date presumably was in the contract when you signed it?
If you now change it, it should be by way of agreement with your vendor. If you can't agree on a new closing date, then there will be a big bunfight, with everyone getting themselves all upset and creating loads of bad feeling. I find that either party in a transaction can be totally unreasonable - in these circumstances, it is often easier , for the sake of peace and to end a potential World War 3 episode to just give in.
March 20th is very tight particularly because of the Bank Holiday.
"he then said his clients needed 6 days notice from when I was in funds to complete before I could move in. I think this is very unreasonable as I will have funds and paying interest and paying their solicitor but can't move in for another week after that. Is this usual?"
I think he meant that rather than aiming blindly at a closing date, that the closing date should be 6 days after you are in funds. The closing date is the date that the purchaser pays the balance of funds due and the vendor hands over vacant possession of the property in exchange for the funds.
mf