If he was on a 250 with L plates and legal, it must have been over 30 years ago as the 125 law came in back in '83.
If all you have is a CBT, then you are limited to a 125, no exceptions, no restricted big bikes, nada. The only time you can be on a bigger bike with L's is when being trained for DAS and you are accompanied by your instructor.
As of January 19th this year, if you pass your test on a 125 you are still stuck on a 125, no L's and you can carry pillions, but still only 125.
To go any bigger you need to take the test on a bigger bike - it all goes by age (17, 19, 21 with previous test passes, 24 for Direct Access) and bike size: 125 up to 14bhp or so, over 395cc between 33 & 47 bhp, or over 600 and over 47 bhp. It's all a bit complicated, so here's the official Govt flowchart you can follow - Click here for a PDF file
Simply put, to ride your XT550, you're gonna have to pass at least the middleweight test - over 19, over 395cc, between 33 and 47 bhp. If you're over 24 just go and do Direct Access, it's the only sensible option .....