Is it legal to place a sign on a private gate which states. 24 HOUR ACCESS REQUIRED NO PARKING.?

As Pema said, in uk it legal as you have the right to access to your property. Although there are certain rules, best to get to a solicitor to discuss this (check out the free half hour that they offer)
I certainly dont think anyone would be arrested for placing such a sign on their property.
yes
It's legal in Uk because parking across someone's drive or garage access is against the law. anyone can park on the street outside your house unless there are parking restrictions clearly posted but they cannot block your drive or garage (ie access).
certainly legal to put the notice up but doubt if you could enforce it if someone parked badly across your gate.
I'm making two assumptions. One, that the gate is yours. The other, that the gate is a driveway gate. You can post what you want on YOUR gate. As long as it isn't obscene or inciting violence. Now if this IS a driveway, and it's your property, you can call the cops if somebody parks on YOUR property without permission, and the car will be towed, at the owner's expense, and they'll get a parking citation. Even if they park on the street, blocking your driveway, you can have them towed. That's how it's been all my life, everywhere I've been in America.
only if its your property
A No Parking sign is enough
It's legal to place the sign but if you do not have a cross-over to your drive, nobody has to pay any attention to it.
If it is your gate, certainly. In any case only a jerk would park blocking a driveway.
It's not legal. Beyond the gate is Public property. It's quite common for property owners to put signs up, but its a matter of courtesy only.


Answer:
yes, and also if you were to park blocking the gate you could be stuck for £60 and 3 points or even have your car towed away by the police for causing an obstruction