I also live in NE London (well an N postcode but its NE on a map) and only generally consider a hotel if its a very very early flight, so 7am or earlier. In those cases I've used both Sofitel and Thistle, both are fine in their own ways, money no object I'd go for Sofitel but Thistle is fine, just be aware that time from room to pod can be 10 minutes or more depending on where your room is exactly, its a bit of a maze in there.
For a departure at your time of day however I'd go for an Uber, checking my last few trips its been £33-35 and takes 45-75 mins, probably 45 at that time of day.
So assuming Thistle gives 25 minutes longer in bed, Sofitel 45 mins longer in bed, I'd be weighing up the extra costs and thinking if its really worth it...