Querytracker isn't even a UK-focused tool (it's primary audience and listings are US), so it means very little regarding the legitimacy of UK agents.
However, The Lindsay Agency has solid-looking sales on its website and works with reputable co-agents (The Rights People). Sales include publishing names I recognise, like Nosy Crow, and their Twitter feed clearly shows that their books are stocked in major UK retailers and getting awards attention.
Submission guidelines are decent: no reading fee, yay. It does directly mention an editorial service that they recommend, but that isn't a red flag so much in the UK as in the US (a lot of the big agencies work closely with places like Cornerstones Editorial).
Guidelines don't mention if they're UK-only or accept international subs, so I would assume they take international subs until told otherwise.
Overall, they appear to be a fairly standard successful UK agency.