You're not going to be able to do this. (I would imagine the Data protection act probably makes it impossible).
The only person who is going to be able to give you the MOT number is the person who owns the car. And you don't know who they are.
The only people who can search the DVLA database for this kind of information are the DVLA and the Police.
You can do a search on the DVLA website but all it will tell you is if the vehicle is registered.
Sorry to be the bearer of bad news.