They could but they will not.
I was looking at an item available at the main Harrods store at Brompton road and I tried to arrange pickup at the Harrods in Heathrow. The main Harrods store redirected me to the Reserve & Collect Team at Heathrow which have claimed this is not possible and they said there's no service to do this.
Closest to Heathrow, I am not sure, but probably the DHL Service Point LHR1KI.
https://goo.gl/maps/2KW86F3vAS3zreiw5 (on the way back, Google is totally drunk suggesting a long roundabout walk, disregard, just walk on Bath Road, there is a sidewalk, you can even see it in Street View)
And as the comment suggest: do not even think doing this on a four hour layover. Maybe previous years you could risk it but even then it'd be risky but in 2022? The EU no longer applies a modicum of sanity to UK security procedures and you have staff shortages. I would avoid security at any UK airport like the plague. (Although, as we have just seen, even that saying is deprecated. Madness rules this world.)