If the towel rail is anything like mine (I have 5) you will find that you will have to have the lockshield valve almost fully closed (mine ended up at quarter turn as it's essentially a load of 15mm pipes in parallel on a 22mm double manifold. normal rads have much thinner channels and higher resistance to the flow of water and on mine the lockshield us at anywhere between 3/4 to 1 1/2 turn depending on distance from boiler and size of radiator.
Your biggest problem is going to be finding microbore equal tees. I've never seen any. You might have to get creative and use a reducer the wrong way into a 15mm equal tee and then use two more reducers to the rads.
This will involve a blowtorch as they all tend to be solder fittings rather than compression fittings.