My understanding is that despite passing a skills test, you don't have a license until it has been issued. So it's not a case of the flying club not 'letting' you fly solo until they've seen the license, the fact is you don't yet
have a license. As you can imagine, there would be legal implications (think of aircraft insurance) if you went flying having passed your skills test for the CAA to then find out that something in your logbook doesn't add up and you fail to meet the criteria to hold that particular license.
I like the temporary license idea, I think that the issue though is all in the law (in this case, the ANO). The CAA are the regulator, they have no power to change what the law states - to change the law you'd have to start with an MP and move on from there.
Which, as the Civil Service also get Maundy Thursday off as an extra "privilege day", means that if you haven't had your licence tomorrow you might as well book some instructor time over Easter as the only way to get in the air ...
I don't think the CAA counts as civil service seeing as they don't receive any money from government and are self funded as such?