yes we do have some minimum turnaround times, the 319 is 35 mins, 320 40mins whilst the absolute minimum is 45 mins for a 321.
As you said it yourself these timings are very tight, especially when there are Customers who need assistance disembarking/boarding or when the CE configurations changes drastically.
And that are mainly the reasons why Boarding does not start when it should be on both outstations and LHR/LGW.

BA wants to work the aircraft harder in future, hence a lot of frontline staff are being sceptical about reducing turnaround times as it will simply mean more delays