No, it isn't normal.
The power drawn by a computer is very low in comparison to what a standard 13A plug is able to deliver.
I suggest the first thing you do is check the fuse in the plug. Quite often these are not changed from the standard 13A which these "kettle plugs" are usually supplied with. The correct rating for a computer is 3A.
If the fuse is wrong, you change it to the correct rating. If it blows then there is something very wrong which you should get checked out by a professional.