bad tenant

Rent Arrears

I let a house to a young Mum with 2 kids on 21st June. I was paid a quarter of the deposit and due to collect the remainder this week. However yesterday I had a complaint from the neighbour saying tenent is throwing dirty nappies and other disgusting sanitary rubbish into the communal back garden which people generally take pride in and look after. She has unsuitable people round all the time and swears loudly at her children for all to hear. Thy want me to give her notice. I agree. mUST i geve one months from today or 2 or as I havent had the full deposit yet is the agreement even valid. Please advise as I must go there soon and try and sort this out.