FYI
I'm seeing the UK London Thai Embassy website has updated there website too reflect the online Visa application system starting 1st April.
It appears now that ANYBODY applying in the UK and not just UK and Irish passport holders will now have to use online application.
The cost of visas increase too from 1st April.
TLDR : Answer Summary
The Thai Embassy in London has updated its website to indicate that starting April 1st, all visa applicants in the UK, regardless of their nationality (not just UK and Irish passport holders), will be required to use an online application system. Additionally, there will be an increase in visa fees effective from the same date.