I don't think that would be `legal'. Strictly speaking, Mum buys a two-tone and then sells it to her son and she would therefore be breaking the law.
For Mum to get into trouble they would both have to be pretty stupid. First the kid (under 18 year old) would have to do something to attract the attention of the police = wave it around in a public place etc. Then, when the police interview said kid, and ask him if it is his gun and how he got it, he would have to reply "I gave my Mum £100 and she bought it for me". Just saying "my Mum bought it for me" would avoid any problems.
Trouble is, when they ask the same question several times in slightly different ways, you start to wonder how much common sense they have.