I work 2 days a week and there's a chance I may be handing my notice in next week. However, after the Monday I will be on annual leave for 1 day next week and 2 days for the 2 weeks following that. (I only work Mon & Tues) Does that time count as part of my 4 weeks notice?
Yes I would expect paid holidays to count as part of your notice.
After all, if the boot were on the other foot and the employer wanted to give you 4 weeks' notice he would probably make you take any outstanding holdiays within your notice period.
However you have to give the notice before the week starts not part way through the week
You can give your notice in on any day you like as the notice period of your contract would start on that day - annual leave does count as notice period but as it is beginning of year the allowance would be pro rated down to what you are entitled to so far so you may end up taking more than you are entitled to and owe money from final salary to the employer depends when the company annual leave starts and ends