Dynamics of interest rates, exchange rates and bond prices within the UIP
One possible flaw in your reasoning is your assumption about what happens to bond prices when there are capital inflows.  For example , suppose that the Bank of England has fixed short term interest rates at 1%, and that the yield of 5yr gilts is also 1%.  Then there is a sudden unexpected rise in the Bank of England rate to 1.5%, resulting in capital inflows to Sterling investments and thus a rise in the FX value of the pound.  However, the short term interest rate is still 1.5% because it is fixed by the BoE, and the 5yr gilt yield is likely to settle at a yield much higher than 1%, depending on the reason for the interest rate raise.  If the BofE says there will be a series of hikes, this yield could settle at 2% or higher.  If the BofE says it is a ‘one and done’ hike, it could settle lower, say 1.25-1.50%.  These numbers are all made up, the point being that it is unlikely that the bond yields stay at 1% when the BofE has raised its short term rate, which appears to be an assumption you made.