Another opinion here. I'm in the USA so things may be a little different, but the basic principles are the same.
1. NO, water flowing from the valve discharge IS NOT NORMAL and indicates a problem with the valve.
2.The Plumber MAY be right about the valve needing to be replaced.
3. The quote sounds to be normal, although too high for me.
4. IF your local codes or ordinances allow it, then YES, YOU CAN FIX IT YOURSELF.
Here are some instructions and hints on doing the job, IF you are legally allowed to do so.
The Temperature and Pressure Relief valve [commonly refered to as a T&P valve here] is designed, intended, and installed on water heaters as a safety device to prevent mechanical explosions from overpressure caused by a failed thermostat allowing the burner to operate to the point of generating steam and hazardous pressure.
The valve design has both a spring to allow the valve to open above a certain pre-set pressure, AND it has a thermal sensing capability which does the same thing above a certain pre-set temperature.
Over time, fluctuations [pressure "spikes"] in the municipal water mains can cause the valve to partially open periododically. This can allow sediment or other small debris normally present in our water systems to become trapped on the valve seat, thus preventing the valve from fully reseating. This results in some leakage from the discharge pipe to the outside.
Also occassionally, the spring can weaken, or the temperature sensing ability can degrade, allowing the valve to open prematurely.
Before replacing the valve I suggest a simple exercise to clear the debris and allow the valve to reseat properly. IF debris is the cause of the leak, then flushing will stop the leak. IF the valve or temperature setting have become defective the leak will continue and the valve will have to be replaced.
To flush the valve and dislodge debris I move the test [flush] handle to the full open position for a few seconds, and then quickly/forcefully SNAP it back to closed so as to seat it firmly. I repeat this several times and then go and observe the other end of the outlet drain line. IF debris was the leak cause, AND if the flushing exercise was successful in clearing the debris from the valve and seat, then the flow will have ceased.
Recheck the outlet for dryness the next day [the time is to allow the water from your flushing/testing to dry up], indicating the valve is sealed closed and not leaking any longer. If after 24 hours the valve is still leaking, then try the flush exercise sequence again. IF the leak is not stopped, then the valve will require replacement as [to my knowledge] they are not capable of being "overhauled or rebuilt."
Assuming that your local plumbing codes/ordinances/laws allow you to do your own plumbing work and replacement of the T&P valve, it is a simple process if you are handy with tools and mechanical procedures.
You will need a new valve, a round wire brush to clean the pipe threads in the heater port opening, either some Teflon Plumber's Thread Tape, or some liquid Plumbers Pipe Thread compound [often called Pipe Dope] , and a wrench or two [here in the US, our T&P valves have hexagonal flats on the valve so we can use a "Crescent" or adjustable wrench, or even the proper sized "open-end] wrench. It is also possible to use a "Pipe Wrench" but I prefer to avoid them whenever I can. Once the materials and tools are at hand, you can then proceed to remove and replace the valve.
First, turn off the water to the heater. IF you're LUCKY, there will be a valve in the incoming cold water line within a foot of the heater top. If there is no valve, then you will have to turn the water off at the main entrance, usually near the water meter location.
Once the water supply is off, you need to open a hot water valve at the kitchen sink, or a bathroom lavatory to allow air into the system to allow you to drain a gallon or so of water from the heater to prevent flooding when you remove the T&P valve.
Once a "vent" is created from above then place a bucket or pan beneath the bottom "drain" valve on the water hearter. Open the valve and drain about a gallon or two of water. Close the valve securely enough to prevent any leakage.
Next, using an old paint brush or a broom, thoroghly clean all debris and dust from around the point where the old T&P valve is screwed into the heater.
Then, using your wrench[es], remove the T&P drain piping from the old valve, then remove the old/defective valve from the heater, and using the round wire brush, clean all debris [old pipe dope compound or Teflon tape from the threaded opening in the heater.
Then wrap THREE or four layers of Teflon tape around the male threads of the new T&P valvle and gently screw it into the water heater, being careful to keep it perfectuly perpendicular to the heater opening to PREVENT CROSS THREADING!!!!!
When it has screwed in at least 3 to 5 th