Hi Madeleine - you can post again next week but I suspect the wait will be longer than that. Wait times for referrals such as this re adverse possession can be lengthy, 3-4 weeks.
And if more is needed and the usual wider checks required then the wait time will be longer also. You/your conveyancer will need manage expectations as appropriate as I suspect exchange/completion should be a little way off yet.
Please read this thread for a better understanding of possible timescales -
Adverse Possession - Claimed Land - Impact on Timescales · HM Land Registry
NYK515954