If I purchase shares in my employer's business via share purchase plan, and those shares are bought directly from my net pay - do I need to pay tax on the money I receive when I sell those shares on the market?
If you sell your shares for more than their value at the time you received them (i.e. you make a profit) then you will be liable for capital gains tax - but only if the profit exceeds your annual allowance (£11,100, in tax year 2015-16).
This is unrelated to how you came by the shares in the first place.
(Note that there are certain exemptions to this, which includes some employer share schemes.)