No one likes a loose rear end, especially after a hot curry.
All 4 tyres at the same pressure as per the sticker on petrol flap?
Sounds like worn dampers to me. If it's on OEM suspension, the gas tends to leak out of the dampers way before they start to leak oil. Can be front or rear, or both.
Anyway, worn parts at either end can feel like it's the opposite end that's gone bad, if that makes sense. A good example of that is warped rear brake discs causing a vibration at high speeds, which a lot of people chase their tale with front wheel balancing/front disc replacements.