As an former HE parent and now HE Grandparent - we love the sound of this type of thing but the nature of HE means one parent always having to be at home therefore money is often tight for many HE families. Also we love the freedom of not having to be in set places at set times and limit the number of on going activities we do. There are many different approaches and attitudes towards education within the HE community and people would want classes that fit with their ideas of education.
Therefore most families want to dip in and out of this type of provision and only a limited number commit to a on-going outlay of money - and this is predominantly for English and Maths with languages and science less popular.
I think the number of parents who would pay for tuition in any of the rest of the curriculum is very small. As mentioned most parents find the education side easy and just want outside involvement occasionally to double check they are covering the basics.
It may be worth thinking about just running English and Maths specific classes as these are by far the most popular. However i have to say we have 4 different classes running within 10 miles of us already offering maths and English tuition and all struggle for numbers. Only around 1 in 10 of the HE families we know use external classes for this type of thing at all. We are reasonably typical in tending to pay for tuition when we need extensive equipment - e.g. Horse-riding, Falconry, Gymnastics.
To give an example of how many people work - Near us we have someone running science classes but we do not want our children to attend all of them just those most relevant to what we are talking about at home or those the child is particularly interested. If we had to commit to all of them we would not go at all.
You do not mention what age you are looking at as GCSE level there may be more demand.
You do not mention where you are as there may be more demand for this type of provision in wealthier areas. We live in the Midlands and we have far too much choice already of activities and groups.
The only way is to advertise the classes and see how many people book on - but if I can be brutally honest I doubt it would generate a real wage and you may barely cover your costs - unless you are extremely lucky with the area you live in. Someone near us has started drop in sessions on all sorts of topics - all with AQA certificates attached and she is still running at a loss after 2 years.
In addition unless you already have links into your local HE community you may well struggle - Tinuveil - who commented above clearly had those links to start her off. We can be a right suspicious lot!!!!
Therefore I guess I am saying that there is a demand for this in the HE community but it is probably far smaller than you might imagine and the cost would be a barrier for many people.
I feel like I have been very negative about your idea but honestly there is not a massive demand out there - most HE families are doing brilliantly and not struggling to provide everything their child needs so you would need to be offering something that they cannot in order for them to part with their money!!!