Not sure if this is the right place to post this.
On several occasions I have had a missed call on my mobile from a number I don’t recognise..when I try to call the number back I get a message saying the number is not recognised..how is this possible?how can the caller display show a number which doesn’t exist ?

It is important to remember that the number shown on screen is merely a "presentation number" and in some circumstances can be altered by the caller. The main use for this is for outbound call centres to present a central inbound telephone number for all callers to call back on, rather than showing the individual telephone number of the particular telephone line that originally made the call.

Scammers and fraudsters also have access to the same sort of facilities and often use it to set a fake telephone number as the "presentation number" in order to try to hide their tracks. The number may have too many or too few digits to be a valid number, may be a number in an unallocated number range, may be a number in an allocated number range but where the individual number isn't currently in use, or may be a valid and operational number that actually belongs to someone else.

The number shown on screen can never offer any sort of guarantee as to the identity of the caller.

Given the prevalence of "wangiri" missed call scams, it is not a good idea to call back to any premium rate numbers starting 084, 087 or 09 or to any international numbers as this could result in considerable call charges being incurred. Discretion is advised with all other numbers. Never call back to any number if you have no idea who you are actually calling and never take their word for it if they tell you who they claim to be.

If you type an unknown number into google it will often reveal something. Sites like whocallsme have extensive lists of scam numbers.

Yesterday I had 2 calls while I was out. Checked both numbers. One, a valid mobile number, was being used by scammers. The other appeared to be a big publisher of trade/techincal magazines. I don't think I have any subscriptions with them. If it's something important and the displayed number was genuine I'm sure they'll make contact again. Otherwise both ignored.

To echo Ian's reply: Never phone back an unknown number.

Those sites present various anonymous opinions about a presented CLI and cannot be relied on for all the reasons mentioned above. It is best to treat all unknown numbers as suspicious. Imagine typing your own telephone number in to one of those sites and reading reports suggesting the number is a known scam - because someone else has been spoofing your number when making calls. The reports are not a true reflection of the whole reality.