Have a slight constant rumble noise from the rear end which seems to increase in volume and pitch on the overrun.  Local garage checked wheel & half-shaft bearings and said they were OK.  They suggested that I change the rear tyres which while legal were pretty worn.  New tyres fitted, but no difference.  Could it be the diff, and if so are there any oil additives I could use - obviously reluctant to shell out for a new unit. Also have a broken rear nearside spring so getting both sides replaced tomorrow, but I don't think that would be responsible for the noise.

Check diff oil level. Filler plug on offside near the top. Oil should be level with filler hole