If you run an engine low enough on oil that it won't rev properly, that's because it's beginning to seize. This causes irreversible engine damage.
If it was leaking that much oil you'd have noticed it, I had a range rover for a while, the puddles **** you off before the oil level drops to any noticeable degree. Land rovers leak, they kind of mark their territory.
Anyway, I'm guessing that since it appears to be consuming alot of oil it's probably breathing quite heavily, take it for a drive until warm and remove the oil filler cap while it's running, some cars splash a bit of oil out which is normal, there if there's alot of oil mist then that's not good. You shouldn't be seeing mist / steam / smoke out of the oil filler cap on a healthy engine (Well not a visible amount)
Why didn't you check the oil and water when you bought it? Low oil level and especially old oil bottles in the boot is a very bad sign.
A modern car engine shouldn't use any oil between services, you should keep a regular check but only really expect to have to top up when you're reaching very high miles (150k or more) and even then, a well serviced engine will last in excess of 200k miles without noticeable oil consumption.
Realistically speaking a litre of oil between services is on the heavy side.. topping up most weeks to keep it running means you've either got a serious leak or you need an engine rebuild.