19 is in relation to where the agency or hirer becomes the employer. This is not the case if you contract to the agency or hirer via a UK limited company as you are the employee of that company NOT the hirer or agency. Have a look at ALL the legislation with regard the right to work in the UK and you will see everything relates to the employer being responsible for this check...even the risk of a £10K fine which the request from the agency boils down to. Quite often these requests are instigated by an employee of the agency who does not fully understand the law, indeed they are just doing their job and requesting the passport copy.
I have contracted via my own UK company on many occasions. I likewise am not happy to have a copy of my passport winging it's was to some Indian office for it then to be sold onto the black market for a few rupees. Your data is not safe in their hands and you are within your right to politely refuse their request for a copy of your passport and offer to show them the actual goods on the day you start your contract.
However, if they or the hirer will ultimately be your employer then I suggest you photocopy it and use photo editing software to embed a BIG watermark across the photo such that you will make it less attractive to be sold on for later use of ID theft
It's standard for an agency to do this (get a copy of passport or driving license) to comply with The Conduct of Employment Agencies and Employment Businesses Regulations 2003:
Confirmation to be obtained about a work-seeker
19. Neither an agency nor an employment business may introduce or supply a work-seeker to a hirer unless it has obtained confirmation -
(a) of the identity of the work-seeker