No, unfortunately, visitors to the UK are restricted to a total of 30 days of study during their visit, and children on visitor visas are not allowed to enroll in government-run state schools. It might be possible for him to attend a private, fee-paying school, but that would likely be extremely expensive (i.e. thousands of pounds per semester/term).
I have struggled finding a sponsor to get a Tier 1/5 Visa and so i am trying to consider all options.
How long have you been looking so far? I only ask because it's not a short or easy process to try to find sponsorship... it can take months, or even years of searching to find a sponsor for a visa (if you are able to find one).
There's no point looking at Tier 1 visas, because several of those options have been closed now and the majority of people cannot qualify for the remaining available options anyway.
- The Tier 1 (General) visa route was abolished a few years ago and is no longer open to new applicants.
- The Tier 1 (Entrepreneur) visa is only open to people who have access to either £50,000 or £200,000 in investment funds to set up or work for their own business in the UK.
- The Tier 1 (Investor) visa is only open to people who have at least £2 million to invest in business in the UK
- The Tier 1 (Exceptional Talent) visa is only open to people who have been endorsed as a leader or a emerging leader in science, humanities, engineering, medicine, digital technology or the arts.
Tier 2 visas might be a bit easier to qualify for, but you would still need to be working in a specialised, highly-skilled or in demand profession to be able to get sponsorship.
Tier 4 Student visas and Tier 5 Temporary Worker visas are probably the easiest options, though in order to bring your son with you on a Tier 4 Student visa, you would have to be studying for a masters degree or higher.