Ok,
You have already found the problem,
lots of one eyed dogs do not bump into things, I've had blind dogs that don't,
you will have to work as a pack(family) team on this, everyone as with all dog pack training have to do the same, consistence is always the key in dog training.
However, he's always pushing past us and barging through. It's annoying in the house but not a huge problem
Yes it is a huge problem as he doesn't realise it is unacceptable, It has to be unacceptable everywhere, it will be easier for him to understand if it is unacceptable everywhere,
when you come home or are leaving home do you make him sit while all the other pack(family) members go through the door?
You must do this, it really important message, he must know to wait for all who are superior to himself within the pack to proceed before he can move on, once given command,
If he does push pass you anywhere ,you must make him come back, sit and wait, EVERY time, if you do this consistently he will get the message eventually(given it is a greyhound it won't be instant),
when you are out and about and he knocks into someone, he must instantly lose his freedom for at least 10 min. recall and put on lead, repeat each and every time he knocks into anyone,
You do feed the dog after all other pack members have eaten?
You don't hand feed?
you don't allow upstairs?
You don't allow on furniture?
It's essential that the dog decides that he is going to make an effort to be aware, at the moment he has no reason to make that a priority, once he has put it to the top of his list of important things to remember, he will no longer knock into humans, at the moment he has no intention to make an effort,
He should be very conscious of his place in the pack(bottom), if he is knocking into the children he is not, you must take that seriously.