HE when a single parent is difficult if you will need to rely on benefits - if you are on UC it can be particularly difficult due to the work commitments you have to comply with in order to be eligible for the benefit.
You will have some options - if you care for someone who receives DLA/PIP you will not have to look for work - to be honest from my experience this is how most single parents on benefits who HE are able to fund it. Alternatively the parents are entitled to disability benefits and it is accepted they are unable to work. As you are currently working and have not mentioned disabilities I am assuming this would not be the case for you.
You can work part time - at any time of the day and claim childcare for your child during that time or use family - depending on your situation. As long as you earn the basic work allowance which roughly equates to minimum wage for 16-20hrs per week - you need to check what yours would be - you will be able to claim UC to top up your money and will only have to attend the job centre every 6 months to explain what you are doing to find more work.
However, you can only work when you have adequate childcare and they CANNOT suggest school as childcare, therefore these 6 monthly interviews are not an issue. I know a few people who do this and it works well for them
If you are currently receiving tax credits and this would not mean a switch to UC - get advice on that - then you can become self employed at something you do from home or around your child and you will get some earnings and tax credit top ups. UC is incredibly harsh on any self employed people - you only get 1 year to get your business up to a level where you earn the equivalent of NMW for 35hrs per week or you will have to seek additional paid work.
So the old method of being self employed that worked for many many HE families is no longer a realistic option for most people.
If you are currently working your best bet is to see how you could fit HE in around this - can you reduce hrs, can you get childcare?
Most people we know who receive DLA for their children or PIP for themselves are reasonably comfortable but the few people we know who are on benefits without disability premiums are vey limited in what they can afford.
But HE can be done very cheaply, you do not need expensive days out or classes. Most education can be done at home by yourself and many of the social groups only cost a couple of pounds so affordable for everyone - however, my daughter has a car and spends a lot on petrol travelling around - so this needs to be factored in as well - depending on where you live.
So basically - long term being on benefits without working is not an option unless there are disabilities or caring for someone with disabilities involved. You will need to work but this only needs to be part time. Think about how you could make this work. Engage with your local HE community now - just put your local area and HE into the facebook search bar - see what is going on locally and maybe talk to a few people. We know our Job Centre work advisors are actually stumped when people talk about HE and the difficulties finding work and tend to get them out the job centre as quickly as possibly and do not take action. But in the neighbouring town people are having a very different experience. Get some proper benefits advice.
There is a group on Facebook for single parents who HE which talks a lot about benefits and how to do it - might be worth searching for that
Ignore any comments about claiming benefits - despite my daughter receiving significant amounts of benefits it is still costing the tax payer far less than providing the school places would.