.. No problems flying over the channel and the former restrictions, mainly uncomfortable altitudes for crossing, have been eliminated anyways.
When did that happen, what are the new rules?
As for a PPL making the long crossings, as said above get some straight and level training. Twice on the Weymouth to Jersey crossing with good VFR forecast I couldn't see a damned thing thru the sea mist apart from the odd glimpse of the whitecaps.
A few years back I was talking to an ex BA captain from Belfast who flew his RV regularly across the water to Scotland, me being a novice asked him what he thought the best crossing altitude was. He was of the firm opinion that no more than 200 AMSL was his preferred height because if the engine quits he did not want to endure the long period of time it took gliding down from say 8000 while running the bitter recriminations and regrets about life including cursing his ex wives and girlfriends over and over while dawdling along at best glide. He'd much prefer going straight into the drink and be done with it.