I have extremely loud banging or screaming machinery almost every weekend around 7 a.m. and barbecues in the evening, which they light next to the fence near my patio doors. They have every machine imaginable and some which disturb people in houses a long way from mine. These are the same people who tried to pull up established shrubs in my border by leaning over the fence - shrubs not higher than or growing into the fence which is mine. Now they have planted many leylandii against the fence which are already about 9ft high, way higher than the 6ft fence panel and growing so fast they are pushing into the fence bending it already. I cannot imagine taking them on about it though, since the woman is aggressive and threatening. I just ignore her.
I have lovely neighbours on the other side, approx same age as the unreasonable ones. Naturally they cut their grass too and sometimes saw up old trees at weekend but they have always said they hope it doesn't disturb me and they do it when we are all up and about, not 7a.m. or 9p.m.!
I would ignore your neighbours for cutting the lawn during the day, since they have to do it sometime and the weekend is probably the only free time they have. If they regularly do things needing loud repetitive banging or use very loud machines which are not the average garden type most people have, or if they make a noise at unsociable hours when people are in bed, that is different. You may even have some other neighbours who are disturbed by it to back you up.