Would this be a red flag to you?

ThisIsWeird

If the house is a semi or terraced, then it should be very straight forward to determine where the exact boundary lies.

That there's no fence present at the moment is a bit strange, but there will be a simple reason such as the two neighbours couldn't be bothered!

When your conveyancer gets sight of the deeds, it'll likely become clear which boundary you will have 'responsibility' for, but there still won't be any requirement to put up a physical fence - very very rarely can this be enforced; if someone doesn't want to, there's little you can do about it.

Of course, most folks will want a fence, and this can either be agreed with the neighbour - and possibly positioned straddling the boundary - or just undertaken by one party. For the latter, it's probably best for that party to set the posts so that their back edges sit right on the boundary line (as best worked out), so the whole actual post and fence sits within your own land - that will make the fence 100% yours.

Claire, what are the other neighbouring houses like - do they have fences or walls?