For the past couple of nights we have had nusiance calls at around 04:00 in the morning.
On our caller ID it usually says "Number unavilable" or it will display this really odd number: 08888888.

Does anyone know what this number means?

I know this won't help, but with VOIP, anyone can put any CLID on a call now. Basically, the number is a spoof, and means nothing.

I only use VoIP (and mobile) for my calls, as I dumped the landline, I can if I wish and have done so in the past few years spoofed the number I was dialling from, using fictional numbers used on TV programmes when calling friends for a laugh, or using my mobile phone number if I was due to go out, just in case they were out and needed to call me back, they could see it was my mobile number.

I'm not in the habit of calling people I don't know using 0111111111 or 0222222222 or 0121 888 8888 / 0121 999 9999 and then hang up just to annoy people.