I'm not about to join the barricades to fight for our right to use our phones while riding - it seems like a stupid thing to do to me. But it would be nice to see a bit of evidence that such a change would be worthwhile in reducing accident rates.
Or is it just a case of "We're not allowed to use our phones while driving several tons of lethal weapon, but there's nothing to stop them from using their phones. Waaaah, it's not fair"
Also, we know what would happen based on other offences: cyclists would be penalised for the offence far more than motorists because cyclists are obvious, exposed and can usually be stopped by a PCSO, while motorists hide inside their metal boxes with the phone on their lap, in the centre console or tucked in the dash by the speedo.
As others point out, this batch of old fart in limos would probably botch the legislative definition of "while riding" too so you'd be required by law to dismount to dismiss a call or alert, or look at a map on your phone. And, as you say, for what gain? I bet most years that cyclist mobile phone use is not a contributory factor for a single recorded road casualty other than the phoney cyclist. We already have a bigger incentive not to futz with phones too much: crashing bloody hurts pretty much every time, unlike for motorists with their bumpers and airbags and crumple zones.
If the Baroness would like to improve road safety, she could do much more good by challenging the crazy situation of parking on pavements (outside London) or most cycleways not being in itself an offence and not generally being accepted as evidence of pavement driving (which is an offence) or highway obstruction, and only roads policing unit officers usually being allowed to stop motorists. That shoot puts walkers and cyclists on the carriageway unnecessarily every day, including bits that are so farking dodgy that even our sluggish councils built protected refuges in the highway (pavements, cycleways) for non-motorists.