The four will head off again next weekend with Sweden, France and Portugal among possible destinations, with the aim being to have a closer look at any transfer targets.
Blackwell said in the Yorkshire Evening Post: "We've all been away this weekend and we'll do the same again next weekend. As the chairman has said we are not going to be browbeaten into some of the demands being made by people here, and we're having a look on the continent.
"I'm still putting great stall by British players, but we'll see if we can unearth anything while we are away. A lot are players who have been recommended to us and this is a chance now to have a look.
"We are not going willy-nilly, looking at anybody. We are looking at specific players in specific areas."
A left-sided midfielder is the club's main priority while a centre-half and forward are also areas where the Whites will be looking to strengthen.