The oil light switch is about 7 psi, so it being on for more than a few seconds at idle is an engine killer.
Problems could include, in order of $
Low oil level - but your's is OK
Bad oil filter - for cost of a 90 mile tow and dealer, you can afford to change filter at the house, or if you are not a DIY there are mobile oil change outfits, or a local shop may do this, based on your situation - needing a house call. Or tow to local shop.
Oil pressure can be tested with a manual guage by a mechanic. That would be done both cold and warmed up, at idle and 2500 RPM. This will also confirm that the $20 oil pressure switch is indeed "good".
If oil pressure test confirms, oil pump would be a candidate for replacement. Could also be blocked pickup screen inside oil pan.
If things have gone on for a great deal of time you may be looking at rebuilding the engine (dealer does not want to do this), or putting in a used or rebuilt one. Rovers are not too complex, you might be able to find a local mechanic to do some of the basics.
There have been recent posts about oil pumps, I'll try to add links to those.
Oil pump/timing chain overhaul/ aftermarket gauge instal,
'03 within VIN range. oil pump cracked-remove dowels?