Dave St Ives is right.
Firstly keep lots of notes on what they are doing wrong. If anything goes to court this is your evidence and will reduce any payout if there is one.
Secondly they cannot claim unfair dismissal until they've worked 2 years for you. That means unless they are pregnant, disabled, or classed as a racial minority they have no come back if you sack them. this means yes you will get away with sacking them on the spot for whatever reason you come up with unless they're with you over 2 yrs.
It is recommended for staff that you give a warning, second warning, then possible dismissal, but these can all be done at the same time!
best thing to do is have a chat with them and encourage them to make the decision to leave. i myself love the line 'I dont think you're happy here', and then if they say why hit them with all the things they dont do etc etc and say if you were happy you would do ... they always decide to go when i have those chats with them... and its usually on good terms
