No, this is where fundamentals as we understand them do not apply.
In a situation of unknown as is the current post Brexit, economics are more governed by fear than by reason, the one country springs to mind is Zimbabwe and it’s inflation, not suggesting that the UK will emulate, just thinking how inflation does not mean buying when fear is introduced.
There is a raised level of fear by investors with regard to the UK at present, I cannot see how politicians can alleviate that fear in the immediate future, therefore the outlook for Gbp is negative.
I suspect that the Boe will find themselves between a rock and a hard place, also suspect that they have figured this themselves.