1. If you are given notice and told not to work it, but are paid for the notice period this is "gardening leave" and the pay is taxable. The employment termination date would then be the end of the notice period.
2. If you are dismissed without notice (i.e. the termination date is the date you are told) then you should receive compensation for breach of contract - the breach being the failure to give you notice. This compensation is the amount of gross pay you would have received had you been given notice. Tax and national insurance should not be deducted because it is not pay - it is compensation.
3. The only qualification to 2 is - as stated by BuckyKat - if the employment contract allows for payment in lieu of notice. If that is the case, then tax & NI do apply.
4. If the dismissal is for gross misconduct it can be immediate with no entitlement to notice pay.