Hi. My name is*****'m looking at your question now and will post my answer or ask for more information here in a short while.
Is your business run as a sole trader with your intention being to make your son a partner or is it run through a limited company with your intention being to give him some of your shares in the company?
Leave this with me while I drat my answer. It will take a while so please bear with me.
If you gift a share of your business to your son, that may give rise to a capital gain so you would need to have your business valued to determine that. If the gain is no more than £11,000, then it will be covered by the annual CGT exemption. You could claim entrepreneurs' relief which would restrict any CGT charge to 10% of the post CGT exemption gain. Take a look here for information on entrepreneurs' relief.
Alternatively, you could make a claim for holdover relief jointly with your son, thereby transferring the gain to your son by reducing the base "cost" of his share of the business which might come to fruition if and when he sells his share of the business. Take a look here for more information on holdover relief. You would use this option if the gain was of a size where the tax liability may be too high to afford.
I hope this helps but let me know if you have any further questions.
Yes, you can do that. Believe it or not people do that with property and its all perfectly legal.