I fly constantly and have found that most airlines have a written 5-10 kg (usually 10 kg) limit on hand-carry items and usually a limit of 1 item only.
However I hardly ever find this enforced and that's usually on short, regional trips, rather than longer international flights. Mostly it occurs because the overhead lockers just aren't large enough on regional flights to take larger bags, so I've had to check my cabin baggage at the plane and collect it again at the plane after landing (not a big deal).
Otheriwse, I haven't experienced any problems in the last 5 years and I usually travel with 2 carry-on bags, each weighing around 10-20 kg. One has my camera gear and the other has my laptop and other accessories.
I did have one problem in 2006 at Heathrow where my bags were weighed at the security check-point, but managed to talk my way through that.
However, I mostly fly out of Schipol and use a range of different airlines without problems.
In the last couple of years I've flown with KLM, BA, Singapore, Qantas, LAN, Iberia, Aeroflot, United, Czech, Swiss-Air, JAT, Alitalia, BMI (with problems), Sky Europe, China Airlines, Continental and American (and probably a couple of others I've missed), generally without any issues on longer flights (and no real major issues on the regional trips other than checking my bags at the plane).
If you are worried, the continent seems to be a bit easier on passengers than the staff at the airports in the UK. I've flown into and out of Heathrow, City, Gatwick, Stanstead, Luton and Birmingham in the past 6 months and these seem to be the most difficult in Europe.
It might be worth considering a tunnel ride across to the Continent and then getting something out of Charles de Gaulle and/or Schipol (the Thalys takes about 2.5 hours from Paris to Schipol).