I think there are a number of potential issues. Which does not mean it is not the best approach in the circumstances.
What about the girlfriend/boyfriend on the same course in lockdown together, or the group of housemates who stayed in their University town. Some will be honest, some won't.
And what about those with less than ideal study conditions. One friend is currently hosting an international student who would have struggled to get home. It seems to be working out, although the house is now pretty full with students and adults working from home. (My friend want her kitchen table back!) Some students in that situation will be struggling. Or struggling with living on their own once friends and flatmates have departed.
It will also highlight deprivation. Universities have responded differently, with some setting relatively little work and others setting masses. From what we hear, Imperial are one of the latter, and their exams, at least in medicine, will count. Yet Imperial attracts a good number of bright students from deprived London inner city backgrounds, often from ethnic minorities. It is already known that overcrowding is a real barrier to school students from such backgrounds doing well and in normal times there are various schemes to provide alternative spaces. (Overcrowding statistics from boroughs such as Tower Hamlets are shocking.) Taking an exam in an overcrowded household, perhaps with poor or non existent wifi, would be detrimental. I hope this is understood.