Some of the clothes sold in the UK have a label attached to them and the material of the label seems to be leather. I don't know whether this leather is from an animal slaughtered islamically or non islamically since these clothes are made in countries such as India. If I were to put this in the washing machine, when it comes in contact with water, would the other clothes become najis as well?

If you are sure that it is real leather then yes it would be najis and would make other items najis if wet.

If you are not sure then you can assume it is tahir and no need to investigate.