Can I use a socket conversion unit to split a washing machine socket in order to add a dishwasher?
The answer to that question in Electrical standards is NO!

The problem is that both these machines use heating elements that can cause surge power to heat water. Now if you use(not you but anybody unknowingly) use them at the same time it could cause an overload. Fine- you are protected by 1-The wall plug, 2-The DB Breaker.

Causing such an overload during peak operation of machines can cause unwanted deterioration of equipment and unnecessary load on electrical wires.

There do exist double isolators(the one on the wall with the red switch/light/fuse)(but they are rare) that can be rated separately by Amperage and should not exceed the amperage of A) The circuit breaker in the DB (taking into account that the proper mm2 wire is used) B) The wattage rating of the actual device

I am completely talking theory here based on what I think it should be(but does not mean that is your case)It could be likely that using the single isolator you could use two sockets-but they have to be certified in order to count towards a propel installed wiring system- and only a certified electrician(qualified does not mean certified) can help you out.

BUT

So the forumula is simple Ohm's Law

Washing machine = 1000Watt
How much is a 1000watts? 1000(Watt) / 240(Volt) = 4.2AMP MAX

If I were a gambling man i would bet a 100 bucks your wall isolator is up to 15AMP and your DB breaker is 5AMP using a 1.5mm2 cable. So how could you possibly accommodate another device of a similar wattage.

Another way.
How much is 5AMPs? = 5(Amps) * 240(Volt) = 1200Watt

When we used to install electric water boilers we were required to use 5mm2 solid copper (3500Watt) and 15AMP Breakers and nothing else is allowed to leach of that circuit.The Units had dedicated isolators in the loft near the unit and internal safety breakers.

To elaborate on your question and demonstrate the difference.

What you are replacing is a switch system that "Isolates" electricity in the event of electricity leakage or short circuit. Isolates means it creates a gap in the Neutral and Live at the same time Isolating the device from all electrical currents(Earth should also be isolated but that is another story-and usually is not)

What you want to install is a normal switch.When you turn it on-it turns on weather there is a short or leakage and will not turn off in the case of fault- causes backwards stress to the DB to trip the circuit. This does not Isolate the circuit. It just cuts out the Live, meaning that if for some unknown reason there was electricity pumping back into the neutral.. it could cause a fire or other damage.

The AMP rating is just what it could handle at MAX peak current.

SO..

The simple answers by many would be- Yea use a splitter- it will be OK (and most likely if you call Dave your neighbourhood white man van- he will install for you for a few bob and nothing will ever happen.. but if he guarantees it he is lying.. so don't be fooled.)

But a professional answer will be NO- It wont be OK- especially if your home insurance finds out after it ....

It may sound stupid, and could  cost a bit- but be safe- Rent a certified electrician and demand a certificate of testing once complete and Tell your insurance. 

There can be no maybes in human life - these things cannot be taken lightly- You feeling lucky? Go play euro millions.