Hello!
You couldn't of made me happier! A new member from the UK AND a Greyhound?????? Bliss!!!!!

There are things you need to understand about your dog.
She is the best and most wonderful companion you could of chosen....BUT...
She is used to spending 22 and half to 23 hours of her day in a kennel.
She loves people because that is her nature and they feed her and take her to chase the bunny. She does not love people because they have spent time playing with her or getting to know her.
By nature that suits her.
She does not need people.
She is quite happy with her own company - having yours is something that will take time to get used to. She doesn't need to be played with or asked to play because she is still coping with an environment that is totally alien to her. Most pet dogs will, in such a situation, look to the owner for support and guidance. Your bitch has never had this and is coping by herself, within herself, as she always has.
I would suggest that you drop the play issue - she may never get this concept - for the time being. Concentrate on VERY simple commands such as the sit (it is a total myth that Greyhounds can't sit....they are the most natural of breeds and can do anything that any other breed can, physically, it's the motivation that is the stumbling block). This will build your relationship with the dog. Remember the dog has only ever seen the human as a servant of it's needs - food, running, track. Most racing Greyhounds don't even connect the human to these things!
Give your dog a VERY comfortable bed - not yours or one that looks like yours! - Greyhounds that have been kept in kennels will almost certainly look for a bed that is above ground level by about two to three feet - just like in their kennel - just like your bed! Shut the door!
Food is a major incentive to most Greyhounds. Most, as I have said, have no idea that this can come from humans. Avoid rustling paper or polythene bags - keep biscuits in your pocket. (Remember to put out the dogs daily feed and only take titbits from that.) This can be your saviour with a Greyhound. Your main aim is to get the dog to realise that what you say followed by a reaction from the dog equals something to eat. As an early step to bonding it is great to reward with food any reaction to the dogs name - even if she looks at you. As soon as she takes a step towards you when you say her name you only reward for that, not for just looking at you. As soon as she gets the idea and comes to you for the food, you only reward for her coming straight to you.

You are so lucky.
You have an independant animal that can take care of herself and she knows it. Do not worry about play - she will not even realise that you are capable of playing with her!
Please, if you have questions or problems email me, if you are not head over heels in love with this bitch already I will take her!!!!!!
Only half joking there.....any help you want, email me, enjoy your bitch for what she is and let us all know how you are getting on, please. (Photos would be great!)