I’ve done it the other way around, driven an Italian car in the U.K. Apart from the hairy first five minutes when getting off the ferry (some ports are better signposted than others) as long as there’s traffic on the road you can follow it’s not too taxing and you just slip into it.
In our case it was handier having our own car we know where everything is, the only real hazards are driving at night, where there is no one else on the road and it is easy to drift over to the wrong side of the road, and overtaking, where you need a passenger to be your eyes.
I got my licence in the U.K. originally but found it easy to drive a left hand drive car - I find changing gear and using the handbrake easier with my right hand. Oddly I worry about driving a right hand drive car as have got entirely out of the habit of changing with my left hand (and I’m a lot older now so adapt less easily to such things), so if I needed to hire a car in the U.K. I would probably opt for automatic.
Driving on the continent is a lot less stressful, the motorways and national roads are on the whole less congested and better maintained than the U.K. Cities can be variable, some have hellish ring roads or tortuous one way systems, but sat nav is your friend. Also, plan your route with Via Michelin and print it out in case your phone dies or your satnav goes loopy.
Yes to the bleeper for the motorway tolls, the one we have in Italy is also valid for France (and maybe Spain?) plus there are other advantages such as automatically paying for parking in many town centres.