I am thinking of purchasing a motorcycle in the UK probably a 250. I live in Australia but have a British passport and an British drivers license. I think I should be okay legaly? I would be up for MOT and third party insurance roughly what is the cost of third party insurance ?I am 56.
Also what would I need if I want to ride in Europe.
It seems rather than ship a motorcycle from Australia it might be cheaper and easier to purchase in the UK?
What happens if you leave the country ie you ride Mongolia and yout MOT runs out can you get back in the UK?

You can get something like a 15 year old Suzuki DR250 for £1500-2000 and with a good service it should be perfectly capable of the trip. As long as you have an address registration should be no problem and try a comparison site for an insurance quote.
https://www.comparethemarket.com/motorbike-insurance/
You are automatically covered for all EU countries and a couple of others such as Switzerland for up to I think 90 days but check the small print on that, insurance is available on the border of all countries not covered.
You can have a new MOT at any time even if it has only recently been done so you start with 12 months, road tax, reggo to you can be renewed or cancelled on-line at any time, it needs current MOT and insurance to renew and if it expires on the road you need to declare it off the road to avoid a fine, just tell them it is at it's registered address, nobody checks.
If you are out of the country for more than 12 months keep your insurance running, tax it before MOT expires and book an MOT at the nearest test station to your port of arrival , just don't have an accident in Europe with an expired one.

You can certainly buy a bike but you will need an UK address to register it to. That's the address where the registration document (the V5) will be sent to. Technically that means you are "registered keeper" which is not necessarily the same as the legal owner but to all intents and purposes it's generally taken to mean proof of ownership.

To use or park the bike on a public road there are some things you will need immediately:

• A driving licence showing entitlement to the appropriate vehicle class (for bikes in UK as I recall this is C)
• Insurance, 3rd party minimum. You can buy this online if you know the bike details, use a comparison site like comparethemarket.com or a specialist broker like Carole Nash
• An MoT (annual vehicle safety test that was originally brought in by the Ministry of Transport)
• Road tax, which you can buy from a post office or online via website gov.uk

The police are keen on ANPR and if you don't have any of these you stand a fair chance of being stopped and your bike expensively impounded. When you buy the bike the last owner gets his road tax refunded - it does not transfer to you. So you will have to tax it straight away, running from the first of the month.

So, when you buy check as well as the condition of the bike, (including correct engine and frame numbers) that it has a current V5 and MoT cert. You sign the V5 and enter your address, the last owner then tears the form in half, gives you the right-hand half and posts the left-hand half to the licensing office. Hold on to your half as it's your proof of ownership until the new form is posted to you. When the V5 comes back in your name you can throw the old half form away. There's no fee to pay.

If you need an MoT most bike shops will do the test but if the old one has expired you should call the shop and make an appointment before riding the bike there. No MoT and no appointment = not legal.

When travelling in the EU the rule is that if the bike is legal in its country of registration it's legal in all the EU. Your insurance will normally cover 3rd party in all EU countries. Bear in mind if your MoT expires it can only be retested in the UK, potentially an issue for long trips.

France has some odd rules for bikes but you can google those. Helmet reflective stickers, CE approved gloves and dayglo jackets.

Edit: as Mark says, if your insurance, tax or MoT run out while you're abroad your best bet may be to declare it SORN (Statutory Off Road Notification) which you can also do online through gov.uk - if you don't declare it SORN and your tax or insurance expire you will automatically get a fine in the post, which could lead to a court summons if it goes unpaid. So know your expiry dates and SORN it before! It's unlikely anybody abroad will be too worried as long as you have insurance in place valid for the country you're in. When you come back to the UK renew your insurance and get it MoT'd at the nearest shop to the port, then tax it (you'll need MoT and insurance in place before you can tax it).

Thank you for your help. I am in the process of working out a trip. I like the idea of the Honda crf250l.. You have been very helpful in working out to ship or purchase in the UK.
Many thanks

That whole British system doesn't make a lot of sense...

That's because you are German, and never the twain shall meet.

Every country has its own peculiarities. But fundamentally the licence, insurance, inspection and road tax principles are the same for everywhere. I just told you how to do it in the UK.