On your comment on generic advice as I am not 100% familiar with your brand strategy accordingly I do not like to give "hard advice". There are too many variables.
That said I will do the best with what provided.
In short there are zero SEO tactical advantages to separating content from brand. Perhaps if the content site is a trick to get someone thinking that the branded site is independent and then refer to your branded domain - about the only time I would consider or recommend it. Is that the case? Hence there are almost zero advantages to setting up a separate site. Site maintenance is hard work, and the doubling of SEO efforts foolhardy. Why have two houses if you only live in one? Unless of course you are rich and it is of no consequence.
If I was advising you I would suggest it is not even worth considering. The domain authority for https://www.esl.co.uk is 25 - which is weak for a specialized site. In short you are not rich enough to afford the second house, the main domain is a straw house at present. If the domain authority was 60+ I might be with you. First thing I worry about is susceptibility to competition.
Given such a low domain authority for the prime domain I would be working hard in improving my link profile and domain authority. Every marketing dollar matters. Focus on building https://www.esl.co.uk into a dominant power - at present however a strong competitor coming into your space would have a powerful impact on search - as it would be easy to outrank. That said great looking site, well optimized from my quick look - needs some strong linking work.
Hopefully not to blunt and a little clearer but happy to answer.