No, there are no valid numbers beginning with +44 0.
You will often see numbers written in a hybridized format like +44 (0) 1632 960123, but that is incorrect and confusing, because for calls to the UK from other countries you do not dial the trunk prefix 0.
The UK
Country code +44 is the UK, and +44 7926 is a mobile code, along with the rest of +44 74 through +44 79.
Holsworthy, Devon, UK
Country code +44 is the United Kingdom. Area code +44 1303 (or 01303 in UK domestic format) is Folkestone.
The country code for the UK is +44. The plus sign means "insert your international access prefix here."
Country code +44 is the UK, and +44 3 is an all-UK number.
UK
+44
The country code and area code of Aberdeen, United Kingdom is 44, (0)1224.
That's not a valid number, but +44 1862 is Tain, a town in the Scottish highlands in the UK.
+44
Dialing from the USA, 00 44 would be UK. 00 is the international access code in USA followed by the country code of UK which is 44.