Thank you, and the diagram was super helpful. If I replace the bath trap with an anti-siphon one, do you think I could safely remove that secondary vent? Or would I be better off leaving it?
Cut it.
Cap it.
Fill and empty the bath.
See what happens.

Thank you, and the diagram was super helpful. If I replace the bath trap with an anti-siphon one, do you think I could safely remove that secondary vent? Or would I be better off leaving it?
It's absolutely standard, and vital, in multi storey buildings to have vent pipes so a "plug" of water going down a pipe doesn't pull the traps which are connected to it.
eg:
View attachment 394915
Yours is probably a situation similar.

Thank you for that.+1 - A secondary vent system, in a domestic setting, are no longer standard these days. They were only really employed where runs are overly extended and these days individual vents (AAV's) would now be placed at the head of the run or anti vac traps used rather than going to the expense and complexity of running a supplementary vent system from the stack.
You do need to understand where it is all connected though, so you know everything that may be effected. Just because they aren't really standard these days doesn't mean chopping things out of a systems that is set up that way, wont then create issues.
then the bath trap is dry - you could verify that by a small stick dipstick - coffee stirrer - waterless trap Hep V O on the bath (it's anti vac/non return ) so the lashed up "vent" system is not working.Thank you for that
When I run the sink tap, I can hear very audibly the sound of water running from the bath drain. Could it be that water running down the sink drain is pulling water from the bath trap, which might mean the secondary vent is necessary? Or would fitting an anti vac trap on the bath drain prevent that issue?



I would do that.Could an anti-syphon trap on the sink waste (highest waste point) mean I could remove that vent pipe?

Great. Just so that I’m clear, would I keep the bath trap the same and only change the sink trap?Ah so it was the "old boy" approach.
I would do that.
The bath trap could be one of those with the extended horizontal part of the trap, giving effectively a better "seal " on the trap.

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