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If for such an international move housing is your only (or even main) issue: Congratulations!
Since a recent rule change, which defines that an agent must be paid by the one who engages him/her (and not always the tenant, as ws the case previously), the rental market has shifted away from agents. Thus I recommend you consult classified ads and contact landlords directly.
If you engage an agent (you can find them e.g. on Immoscout24), be prepared to fork out three months rent as fee.
A further note: It is basically unheard of in Germany to rent out a property to somebody the landlord hasn't met in person (and also for you it is far better to rent only after viewing). Thus you can really only start searching after you arrive (and while staying in temporary accommodation, e.g. hotel).
Please also keep in mind that the rental market in Berlin is very hot and it will be difficult to find anything decent especially price-wise) unless you stay outside of the public transport area.

Dear Beppi, thanks for your quick response and most helpful advice. I do have a motor home which, is a form of housing!! However, I also have family living there. I am trying to avoid putting on their time and appreciate your help. I will ask them for local advertising papers and agents. I have the funds ready for a deposit.
Thanks once again.
Barrie (Chef1)

A motor home on private ground of your relatives (as it isn't allowed to sleep in one on public ground - although this is not universally enforced) seems a good option for the beginning.
Just to check if your financial expectations are right: The deposit is normally 3 months rent, you need another 3-months for the agent (if you engagd one) and then the rent for the first month, plus expenses for furnishings and equipment (most apartments here are bare empty, so you need everything from curtains to lamps to washing machine - only fitted kitchens are sometimes present). If you, say, rent a 2-room apartment for EUR600/month (which is cheap!), you thus need about EUR7000 upfront.
Another question: You are British according to your profile. Is it a good idea to move to the EU so shortly before Brexit, with all the uncertainty whether you will be able to stay on (visa-wise) afterwards???

A motorhome is a great thing. It can insure that you have a roof over your head until you find something more permanent.  Or like Beppi mentioned, you could actually live there if parked on private land. The question is where it is registered. If you get residency in Germany I think you will eventually have to change the registration to Germany if it has foreign plates. If you have a UK registered vehicle you might have to pay import duties to change the registration if Brexit actually happens. And most German cities now have an environmental zone restriction. Every vehicle needs to have a sticker that shows its fine particle emission class. Euro-4 with the green sticker is standard now in most cities; Stuttgart is now demanding Euro-5 for diesels and may demand Euros-6 within a couple of years. And yes, even foreign vehicles are affected although I don’t know how they go about enforcing it on tourists’ vehicles.

Beppi is right that it is officially not allowed to sleep in one’s motorhome on public streets but this is rarely enforced. In most places, one just needs to keep a very low profile. But while this is possible in a location for a couple of days one can hardly stay permanently in a motorhome in the same area without drawing some attention. Best to find places some distance to where people live, say on the outskirts of a town or near big parks and to change location on a regular basis. I had a motorhome for 17 years and while I didn’t live in it permanently, I often slept in it and travel for months at a time. And I never went to campgrounds like authorities say one should since they often charge 20 or 30 or more Euros a night just to park! But middle to large cities have gotten difficult as there is often only expensive pay parking or areas reserved for local residents with a special sticker. For even a smalll motorhome, it is hard to find large enough parking spaces and they tend to stand out like a sore thumb in a big city residential neighborhood. Also, some tourist areas like the North Sea or Baltic Sea live off of tourism and want to see that people go to a hotel or campground. There are some towns in these areas where one cannot even park a motorhome on a public street.

TominStuttgart, Thanks for the heads up. I am at present looking at the low emissions certificate for the Berlin area.
Cheers
Barrie

Which fine-particle emission sticker a vehicle gets is not actually done by testing, there is simply a list for all vehicles that they go by. The sticker is put on the inside of the windshield and is recognized country-wide. So the sticker itself has nothing to do with Berlin or any other location, but the cities set the standard which sticker they require for vehicles to be driven there. Berlin currently requires a green Euro-4 sticker.

In some cases there might be a filter system available to qualify for a better level. One has to ask at a car dealership from the brand. For example, my last car had a Euro-3 sticker but there was a filter system available to qualify it for Euro-4. Since the car was over 5 years old (or over 50,000 KM) then I also had to replace the otherwise perfectly good catalytic-converter. Cost was over 1000 Euros. Thankfully, I sold this car 2 years ago because it would now no longer be allowed in Stuttgart where I live. And the same problem can happen in other cities as they start to demand Euro-5 or Euro-6 stickers.

I don’t know the recent trends but a decade or so ago when I had my motorhome about 90% of them in Germany were diesels. If one has a rather high-value diesel motorhome it might be worth looking into having the engine switched for a gasoline one.

If one has an older vehicle one should also be aware that there is a safety inspection done every 2 years that includes another type of emissions’ test. This could be a problem for a vehicle that might have met the standards in a country with laxer regulations.