Which diseases are carried by mice and cat fleas in uk which could cause petechiae in humans? (my 10 month old daughter and 3 year old son have a few)

Not many: Dog and cat fleas in the UK are generally not a source of transmission of serous diseases to humans. They can cause tape worm infestation which would have abdominal to be a sign of serious disease, one would expect the rash to change rapidly and kids wouldnt be feeling well in a short course. In any case, the kids need to be examined to be on the safe side.