Swivel tap sprays water when cold tap turned onl

You can remove the spout from the body and replace the 'o' rings and re grease unless its a sealed unit, in which case it is better to replace tap completely. I hope this helps.

i take it you mean where it swivels ?,new o rings if you can get the right size.

New tap. Scaled up head

Depends on where it is spraying from but sounds to me like a washer